Archive for March, 2012


Systems Of Inequalities Example 1

Here is an example of how to solve a system of inequalities.  Remember to read the lesson on this topic. Basic steps to follow: 1. First make sure you understand how to solve linear inequalities and systems 2. Graph both lines of the system and find the solution; be mindful of the lines you draw; […]

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How To Solve A System By Graphing Example 1

Here is an example of how to solve a system using the graphing method.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that the solution to a system is the (x, y) point where the lines that make up the system intersect 2. Graph both lines as accurately […]

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Systems Elimination Combination Method Example 1

Here is an example of how to solve a system using the elimination combination method. Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that you can solve systems using various methods- this is only one method 2. Take steps such that you get opposite pairs of the same […]

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How To Multiply And Divide Positive And Negative Numbers (Real Numbers) Example 1

Here is an example of how to multiply and divide positive and negative numbers (real numbers).  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that these rules apply to positive and negative numbers on the real number line- “real numbers” 2. The rules for multiplying and dividing positive […]

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How To Add Like Terms Example 1

Here is an example of how to simplify an expression by combining like terms.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand what like terms are; like terms are expressions that have the same variable(s) to the exact same powers 2. Locate all like terms and add them […]

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How To Use The Distributive Property Example 1

Here is an example of how to use the distributive property.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that the distributive property in another way to do multiplication 2. The distributive property is key in algebra especially when you see expressions with parentheses like 3( x + […]

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How To Add And Subtract Positive And Negative Numbers Example 1

Here is an example of how to add and subtract positive and negative numbers.  Remember to read the lesson on this topic. Basic steps to follow: 1. First we are focusing on the positive and negative numbers on the real number line 2. Next to add positive and negative numbers follow the rules; same sign […]

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Direct And Inverse Variation Example 1

Here is an example of how to solve a direct and inverse variation problem.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that variation problems are basically equation problems; know the difference between direct and inverse variation 2. Next use the data in the problem to find the […]

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How To Simplifying Rational Expressions Example 1

Here is an example of how to simplify a rational expression.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that a rational expression is a fraction with variables 2. Simplifying a rational expression means to reduce the expression-think of it as reducing a fraction 3. Factor the numerator […]

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Ratios And Proportions Example 1

Here is an example of how to solve a ratio and proportion problem.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that a ratio is a fraction and a proportion is two equal fractions 2. Identify a fraction from the information in the problem; then identify another fraction […]

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How To Solve A Rational Equations Example 1

Here is an example of how to solve a rational equation.  Remember to read the lesson on this topic. Basic steps to follow: 1. First if the rational equation is a proportion (one fraction = one fraction) than cross multiply to solve 2. However if the rational equation is not a proportion find the LCD […]

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Solve Basic Percent Problem Example 1

Here is an example of how to solve a percent problem.  Remember to read the lesson on this topic. Basic steps to follow: 1. First keep in mind that percent is a fraction where the denominator is 100 2. To find the percent of a number change the percent to a decimal (move the decimal […]

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Multiplying And Dividing Rational Expressions Example 1

Here is an example of how to multiply and divide rational expressions.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that performing operations with rational expressions follow the same steps as operations with fractions 2. Always factor expressions first to simplify before multiplying or dividing 3. Perform the […]

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Adding And Subtracting Rational Expressions Example 1

Here is an example of how to add and subtract a rational expression.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that operations involving rational expressions follow the same procedures as working with fractions 2. Next to add or subtract rational expressions they need to have the same […]

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Radical Equations Example 1

Here is an example of how to solve a radical equation.  Remember to read the lesson on this topic. Basic steps to follow: 1. First write the equation such that you have the radical isolated on one side of the equation 2. Next square both sides of the equation to eliminate the radical 3. Solve […]

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Simplifying Radicals (Square Roots) Example 1

Here is an example of how to simplify a radial (square root).  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that square roots are 1 type of radical expression; cube roots and other roots also follow these rules 2. The key to simplifying a radical expression is to […]

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Pythagorean Theorem Example 1

Here is an example of how to use the Pythagorean Theorem.  Remember to read the lesson on this topic. Basic steps to follow: 1. First the Pythagorean Theorem only applies to right triangles; make sure that one of the angles of the triangles = 90 degrees 2. Next plug in your a, b and c […]

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Operations With Radicals Example 1

Here is an example of how to perform operations with radical and square roots.  Remember to read the lesson on this topic. Basic steps to follow: 1. First know the properties of radicals; multiplication/division are the same and adding/subtracting are the same 2. Next when multiplying radicals- multiply the numbers under the radicals (square root […]

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Mid-Point Formula Example 1

Here is an example of how to use the mid-point formula.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that the mid-point formula finds the (x, y) point that is “mid way” between two other points 2. Next plug in your (x, y) values into the formula 3. […]

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Distance Formula Example 1

Here is an example of how to use the distance formula.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand the distance formula finds the “distance” between two points on the x-y plane. 2. Next plug in your (x, y) points into the formula 3. Simplify the expression using […]

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Solve A Quadratic Equation By Taking The Square Roots Example 1

Here is an example of how to solve a quadratic equation by taking the square roots of both sides.  Remember to read the lesson on this topic. Basic steps to follow: 1. First not all quadratic equations can be solved by taking the square roots of both sides (unless you use completing the square) 2. […]

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Solve A Quadratic Equation By Factoring Example 1

Here is an example of how to solve a quadratic equation by factoring.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that not all quadratic equations can be factored; if the equation can be factored follow these steps 2. Factor the quadratic equation into two factors- i.e. two […]

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Quadratic Inequalities Example 1

Here is an example of how to solve a quadratic inequality.  Remember to read the lesson on this topic. Basic steps to follow: 1. First graph the parabola; find the y -intercept and possible x-intercepts to make the graph as accurate as possible 2. Next make sure the graph of the parabola is solid if […]

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Solve Using The Quadratic Formula Example 1

Here is an example of how to solve a quadratic equation by using the quadratic formula.  Remember to read the lesson on this topic. Basic steps to follow: 1. First write the equation in standard form (from highest to lowest power) 2. Next plug in your a, b and c values into the quadratic formula […]

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Graphing A Quadratic Equation Example 1

Here is an example of how to graph a quadratic equation.  Remember to read the lesson on this topic. Basic steps to follow: 1. First write the quadratic equation into standard form (from highest to lowest power) 2. Next use the formula to find the vertex (x, y) point of the graph 3. Lastly determine […]

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Find The Discriminant Quadratic Formula Example 1

Here is an example of finding the type of roots using the discriminant.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand the discriminant is part of the quadratic formula- the part inside the square root 2. The purpose of the discriminant is to indicate what type of roots […]

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Quadratic Equations Completing The Square Example 1

Here is an example of how to solve a quadratic equation by completing the square. Remember to read the lesson on this topic. Basic steps to follow: 1. First make sure the equation is in standard form- highest to lowest power 2. Next perform the operations to set up a perfect square on both sides […]

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Scientific Notation Example 1

Here is an example of scientific notation.  Remember to read the lesson on this topic. Basic steps to follow: 1. Scientific notation is a method to write very large or small numbers in a power – power of 10 2. The key idea in scientific notation is to move the decimal point of the number […]

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Properties Of Exponents- Power Rules Example 1

Here is an example of the properties of exponents.  Remember to read the lesson on this topic. Basic steps to follow: 1. First know the basics about powers- they have a base and an exponent 2. Take note that to multiply or divide powers the bases must be the same 3. Never leave a power […]

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Exponential Growth And Decay Example 1

Here is an example of how to determine if a graph is exponential growth or decay.  Remember to read the lesson on this topic. Basic steps to follow: 1. Both exponential growth and decay are functions- i.e. there graphs pass the vertical line test 2. Exponential function graphs slope upward from left to right- decay […]

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Compound Interest Example 1

Here is an example of a compound interest problem.  Remember to read the lesson on this topic. Basic steps to follow: 1. First make sure you understand the formula and what the variables represent 2. Common areas to note: the “r” in the formula is the APR (annual interest rate) as expressed as a decimal […]

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Special Multiplication Rules For Polynomials Example 1

Here is an example of how to multiply polynomials using special rules.  Remember to read the lesson on this topic. Basic steps to follow: 1. First only certain special multiplication patterns will have a rule- example (a + b)(a – b) 2. Once you determined the special pattern apply the rule to find the product […]

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Special Factoring Rules Example 1

Here is an example of how to use special factoring rules to factor a polynomial.  Remember to read the lesson on this topic. Basic steps to follow: 1. First try to factor out a gcf from the polynomial 2. Next determine what type of special pattern the polynomial has- i.e. “the difference of two squares” […]

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Factor Quadratic Trinomial Example 1

Here is an example of how to factor a quadratic trinomial.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that you may not be able to factor a polynomial- i.e. the polynomial is prime 2. Next there are a few common methods to factoring trinomials- master the method […]

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Factor The GCF From A Polynomial Example 1

Here is an example of how to factor the gcf from a polynomial.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that there maybe no gcf to factor- a polynomial could be prime 2. Prime factor each of the terms of the polynomial and determine the greatest common […]

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Add And Subtract Polynomials Example 1

Here is an example of how to add and subtract polynomials.  Remember to read the lesson on this topic. Basic steps to follow: 1. First if the problem is subtraction make sure to correctly distribute the negative sign to all terms 2. Next determine what terms are like and not like 3. Combine like terms […]

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Evaluate Variable Expressions Example 1

Here is an example of how to evaluate a variable expression.  Remember to read the lesson on this topic. Basic steps to follow: 1. First replace the variable with the value(s) in the given expression 2. Always double check that you plugged in the value(s) correctly before moving onto to simplify the expression 3. Use […]

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Translating Verbal Phrases Into Variable Expressions Example 1

Here is an example of how to translate a verbal phrases into a variable phrase.  Remember to read the lesson on this topic. Basic steps to follow: 1. Translate the phases by breaking the phrases into sections 2. Know key phrases like “a number” means a variable or “increased by” means adding 3. Take all […]

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Order Of Operations Example 1

Here is an example of how to use the order of operations.  Remember to read the lesson on this topic. Basic steps to follow: 1. First know the meaning of PEMDAS- Parentheses, Exponents(powers), Multiplication, Division, Addition, Subtraction 2. Always start inside of parentheses working from the inside out and left to right 3. Continue to […]

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Basic Number Operations Example 1

Here is an example of how to perform basic number operations.  Remember to read the lesson on this topic. Basic steps to follow: 1. Determine what operation you are being asked to perform 2. Product means multiply; quotient means division; sum means add; difference means subtraction 3. Perform the operation- pay special attention to division […]

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Two Variable Inequality Example 1

Here is an example of how to solve and graph a two variable inequality.  Remember to read the lesson on this topic. Basic steps to follow: 1. First graph the line of the inequality; pay special attention to your line < and > will be dashed lines and ≤ ≥ lines will be solid 2. Select a […]

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Linear Inequality Example 1

Here is an example of how to solve and graph a linear inequality.  Remember to read the lesson on this topic. Basic steps to follow: 1. Solve for the variable just as you would in an equation 2. If you multiply or divide by a negative number you need to reverse the inequality symbol 3. […]

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Compound Inequality Example 1

Here is an example of how to solve and graph a compound inequality.  Remember to read the lesson on this topic. Basic steps to follow: 1. Solve for the variable in the middle of the inequalities 2. Be careful to reverse inequality signs if you multiply or divide by a negative number 3. Look at […]

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Sketch The Solution To An Inequality Example 1

Here is an example of how to graph a the solution of an inequality.  Remember to read the lesson on this topic. Basic steps to follow: 1. Draw a circle at the number 2. Fill the circle in if the solution is ≤ ≥ if the solution is < or > leave the circle open 3. Determine […]

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Graph A Line With Two Variables Example 1

Here is an example of how to graph a line with two variables.  Remember to read the lesson on this topic. Basic steps to follow: 1. Not one way to approach these problems; generally you want to place the equation into y=mx + b form and graph 2. Another way is to find the x […]

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Find The Slope Given Two Points Example 1

Here is an example of how to find the slope.  Remember to read the lesson on this topic. Basic steps to follow: 1. First know the slope formula 2. When plugging in your values make sure they are done in the correct way; order does make a difference 3. Simplify the final fraction Graphing Linear […]

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Graphing One Variable Lines Example 1

Here is an example of how to graph a one variable line.  Remember to read the lesson on this topic. Basic steps to follow: 1. Lines that are x= a number are vertical though the point (x, 0) 2. Lines that are y= a number are horizontal through the point (0, y) 3. Make sure […]

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Function Operations Example 1

Here is an example of function operations.  Remember to read the lesson on this topic. Basic steps to follow: 1. Function operations is when you add, subtract, multiply or divide functions- you can also have any number of combinations of operations applied to one or more functions 2. Apply the operation(s) to each function 3. […]

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Linear And Non-Linear Functions Example 1

Here is an example of the graph of a non-linear function.  Remember to read the lesson on this topic. Basic steps to follow: 1. First identify what type of function you have- example, exponential, log, trig, linear, etc 2. If asked to graph the function sketch the basic graph with a few key reference points […]

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Find The Inverse Function Example 1

Here is an example of how to find the inverse function.  Remember to read the lesson on this topic. Basic steps to follow: 1. First switch the x and y variables in the equation; i.e. the x’s become y’s and the y’s become x’s 2. From the new equation above solve for y- this is […]

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Graphing Functions Example 1

Here is an example of how to graph a function.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand that there are many different type of functions each with specific steps to graph 2. However we can take the basic shape of a function and move it up or […]

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Composite Functions Example 1

Here is an example of how to evaluate a composite function.  Remember to read the lesson on this topic. Basic steps to follow: 1. Make sure to understand the what is the main function; example f(g(x)) the f(x) function is the main function- another words you will be plugging in the g(x) function into the […]

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Determine If A Relation Is A Function Example 1

Here is an example of how to determine if a relation is a function.  Remember to read the lesson on this topic. Basic steps to follow: 1. If the relation is expressed as a set of ordered pairs look to see if each x value has only one y value- this is a function 2. […]

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Multiply And Divide Fractions Example 1

Here is an example of how to multiply and divide fractions.  Remember to read the lesson on this topic. Basic steps to follow: 1. To multiply fractions just multiply respective numerators and denominators 2. To divide fractions flip the divisor (second fraction) this turns the problem into a multiplication problem 3. After multiplying reduce and […]

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Find The LCD of A Fraction Example 1

Here is an example of how to find the LCD of fractions.  Remember to read the lesson on this topic. Basic steps to follow: 1. First write out all the multiples of the respective denominators 2. Look for the lowest common multiple of the respective numbers 3. The LCM of the numbers will be the […]

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Write A Decimal As A Fraction Example 1

Here is an example of how to write a decimal as a fraction.  Remember to read the lesson on this topic. Basic steps to follow: 1. First determine how many place holders the digits of the decimal cover- tenths, hundredths, thousandths? 2. Write a fraction with the numbers of the decimal as the numerator and […]

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Add and Subtract Fractions Example 1

Here is an example of how to add and subtract fractions.  Remember to read the lesson on this topic. Basic steps to follow: 1. First determine if the denominators are common- i.e. the same 2. If the denominators are not common find the LCD and multiply each fraction such that the denominators are the LCD […]

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Fine The Equation Of A Line Given Two Points Example 1

Here is an example of how to find the equation of line given two points.  Remember to read the lesson on this topic. Basic steps to follow: 1. First to find the equation of a line you need at least the slope and one point 2. Use the two points to calculate the slope 3. […]

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Write The Equation Of A Line In Standard Form Example 1

Here is an example of how to write an equation of a line into standard form.  Remember to read the lesson on this topic. Basic steps to follow: 1. First place the x and y variable terms on the left side of the equation; number term on right 2. Next clear any fractions or decimals […]

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Graph A Line Using Slope-Intercept Example 1

Here is an example of how to graph a line using the slope-intercept equation.  Remember to read the lesson on this topic. Basic steps to follow: 1. First make sure the equation is in y=mx + b form 2. Plot the y-intercept b 3. From the y-intercept use the slope m to locate another point […]

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Find Line Equation Using The Point-Slope Formula Example 1

Here is an example of how to find the equation of a line using the point-slope formula.  Remember to read the lesson on this topic. Basic steps to follow: 1. First you will need at least the slope and one point on the line; if you have only two points find the slope and use […]

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Best Fitting Line (Scatter Plot) Example 1

Here is an example of how to find the best fitting line.  Remember to read the lesson on this topic. Basic steps to follow: 1. Look at the trends of the points plotted and determine a line that would “best fit” the trend 2. Select two points off the “best fitting” line you estimated 3. […]

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Two-Step Equations Example 1

Here is an example of how to solve a two-step equation.  Remember to read the lesson on this topic. Basic steps to follow: 1. First understand how to solve one-step equations 2. Take a step to isolate the variable term 3. Solve the remaining one-step equation Equations-two-step-1   Important habits to master math: 1. write […]

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One-Step Equations Example 1

Here is an example of how to solve a one-step equation.  Remember to read the lesson on this topic. Basic steps to follow: 1. Look at the equation and think what step would need to be taken to isolate the variable 2. Take the step you identified above and do it to both sides of […]

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Multi-Step Equations Example 2

Here is an example of how to solve a multi-step equation.  Remember to read the lesson on this topic. Basic steps to follow: 1. Do any parts of the problem that require the distributive property; any place where there is parentheses 2. Combine like terms and simplify both sides 3. Simplify the equation until you […]

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Formula Equations Example 1

Here is an example of how to solve a formula equation.  Remember to read the lesson on this topic. Basic steps to follow: 1. Isolate the variable to be solved for; this is only variable that you will treat as a “variable” during the equation solving process 2. Take steps to isolate the variable you […]

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Absolute Value Inequality Example 1

Here is an example of how to solve an absolute value inequality.  Remember to read the lesson on this topic. Basic steps to follow: 1. Isolate the absolute value function 2. Write a linear or compound inequality; in this step you will be dropping the absolute value 3. Solve the respective inequality and graph the […]

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Graph An Absolute Value Equation Example 1

Here is an example of how to graph an absolute value equation.  Remember to read the lesson on this topic. Basic steps to follow: 1. Find the vertex (x,y) 2. Determine if the graph will be upward or downward 3. Determine how wide or narrow the V graph will be (estimate) 4. Sketch the graph […]

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Evaluate An Absolute Value Expression Example 1

Here is an example of how to evaluate an absolute value expression.  Remember to read the lesson on this topic before you try the problem.  I will give you some basic steps so if you are having problems with parts of the problem go back and review.  For example in this problem you may need […]

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Absolute Value Equation Example 1

Here is an example of how to solve an absolute value equation.  Remember to read the lesson on absolute value equations as well.   Basic steps to follow: 1. Isolate the absolute part of the equation- in this example the absolute value is isolated on the left side. 2. Set what is inside of the […]

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