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Chapter 2: Q30. (page 106)

Solve each equation. Then graph the solution set.

34a鈭�3=9

Short Answer

Expert verified

The equation 34a鈭�3=9has solution set as a=16and a=鈭�8and the graph of the solution set is:

Step by step solution

01

Step-1. Define absolute value equation.

For any real numbers a and b, ifa=b and b鈮�0, thena=b or a=鈭�b.

02

Step-2. Formulate case 1 when 34a−3=9.

Simplify the expression for a.

34a鈭�3+3=9+334a=1234a脳43=12脳43a=16

03

Step-3. Formulate case 2 when 34a−3=−9.

Simplify the expression for a.

34a鈭�3+3=鈭�9+334a=鈭�634a脳43=鈭�6脳43a=鈭�8

04

Step-4. Plot the graph of the solution set.

From case 1 and case 2, a=鈭�8,鈥�16. Plot these values on the number line.

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