# Solving Open Sentences Involving Absolute Value

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Solving Open Sentences Involving Absolute Value
Lesson 6-5 Solving Open Sentences Involving Absolute Value

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Objectives Solve absolute value equations
Solve absolute value inequalities

Vocabulary none

Steps for Solving Equations
Step 1: Use the Distributive Property to remove the grouping symbols, () or [] Step 2: Simplify the expressions on each side of the equal sign “=” by combining like terms (variable and #’s) Step 3: Use the Addition and /or Subtraction Properties of Equality to get the variables on one side of the equal sign and the numbers without variables on the other side of the equals sign Step 4: Simplify the expressions on each side of the equals sign by combining like terms Step 5: Use the Multiplication and/or Division Properties of Equalities to solve for the variable

Example 1 Method 1 Graphing
means that the distance between b and –6 is 5 units. To find b on the number line, start at –6 and move 5 units in either direction. The distance from –6 to –11 is 5 units. The distance from –6 to –1 is 5 units. Answer: The solution set is

Example 1 cont Method 2 Compound Sentence Write as or Case 1 Case 2
Original inequality Subtract 6 from each side. Simplify. Answer: The solution set is

Example 2 Write an equation involving the absolute value for the graph. Find the point that is the same distance from –4 as the distance from 6. The midpoint between –4 and 6 is 1. The distance from 1 to –4 is 5 units. The distance from 1 to 6 is 5 units. So, an equation is .

Example 2 cont Answer: Check Substitute –4 and 6 into

Example 3 Then graph the solution set. Write as and Case 1 Case 2
Original inequality Add 3 to each side. Simplify. Answer: The solution set is

Example 4 Then graph the solution set. Write as or Case 1 Case 2
Original inequality Add 3 to each side. Simplify. Divide each side by 3. Simplify. Answer: The solution set is

Summary & Homework Summary: Homework: If |x| = n, then x = -n or x = n
If |x| < n, then x = -n or x = n (inside) If |x| > n, then x = -n or x = n (outside) Homework: none n -n n -n n -n