2 5 Study Guide And Intervention Solving Equations Involving Absolute Value

2 5 Study Guide And Intervention Solving Equations Involving Absolute Value Study Guide and Intervention Workbook 5 2 Solving Equations with Variables on Each Side 53 5 3 Inequalities unknown value To translate verbal phrases with an unknown quantity into algebraic expressions first define the variable

When solving equations with absolute values there can be more than one possible answer This is because the variable whose absolute value is being taken can be either negative or positive and both possibilities must be accounted for when solving equations Example 2 5 1 Solve x 7 x 7 x 7 and 7 or 7 x 7 and 7 or 7 Solve the equations by graphing If exact roots cannot be found state the consecutive integers between which the roots are located 1 x2 4x 2 20 2 x 6x 6 0 3 x2 4x 2 0 4 2x 2x 4 0 5 2x2 12x 17 0 6 x2 x 0 x f x O x f x O x f x O 5 2 1 2 x f x O x f x O x f x O 2 2 1 x f x O Study Guide and Intervention continued Solving

To the StudentThis Study Guide and Intervention and Practice Workbookgives you additional examples and problems for the concept exercises in each lesson The exercises are designed to aid your study of mathematics by reinforcing important mathematical skills

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2 5 Study Guide And Intervention Solving Equations Involving Absolute Value

1 4 Study Guide And Intervention Solving Absolute Value Equations

Lesson 8 1 Skills Practice Answers Algebra 2

5 2 Study Guide And Intervention Substitution

Solved PERIOD NAME DATE 1 3 Study Guide And Intervention Chegg

Question Video Solving Absolute Value Linear Equations Involving Two

1 4 Study Guide And Intervention Solving Absolute Value Equations

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Isolate the absolute value first Case 1 Case 2 The solution set is 5 5 5 5 62 87 21 Isolate the absolute value first means the distance between q and 0 is 2 Since distance cannot be negative there is no solution 62 87 21 Isolate the absolute value first Case 1 Case 2 The solution set is 2 2

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1 Simplify the expressions inside grouping symbols Order of 2 Evaluate all powers Operations 3 Do all multiplications and divisions from left to right 4 Do all additions and subtractions from left to right Evaluate 18 6 4 2 18 6 4 2 18 10 2 8 2 4 Evaluate 3x2x y5 if x3 and y0 5

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Case 1 The value inside the absolute value symbols is positive Case 2 The value inside the absolute value symbols is negative Solve x4 1 Then graph the solution set Write x4 1 as x4 1 or x4 1 x4 1orx4 1 x4 4 1 4x4 1 x3x4 4 1 4 x5 The solution set is 5 3 The graph is shown below 8 7 6 5 4 3 2 10

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5 Study Guide and Intervention Solving Equations Involving Absolute Value Absolute Value Expressions Expressions with absolute values define an upper and lower range in which a value must lie Expressions involving absolute value can be evaluated using the given value for the variable

Step 1 Evaluate expressions inside grouping symbols Order of Step 2 Evaluate all powers Operations Step 3 Do all multiplication and or division from left to right Step 4 Do all addition and or subtraction from left to right Example 1 Evaluate each expression a Example 2 Evaluate each expression When solving absolute value equations and inequalities two options need to be considered when the expression inside the absolute value is not negative and when the expression inside the absolute value is negative Key Terms Absolute Value The absolute value of a number is the distance of that number from 0 Absolute Value Equations

2 20 2 5 2 20 2 13 5 7 7 7 5 The solution is 40 Multiply each side by 2 c 5 40 For some problems it may be necessary to combine like terms before solving Exercises Solve each equation Check your solution 1 5t 1 2 5 7 2 2x 1 5 5 9 3 6u 2 8 5 28 4 8m 2 7 5 17 Lesson 3 5