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Chapter 2: Q38. (page 106)

Solve each equation. Then graph the solution set.

鈭�4d+6=12

Short Answer

Expert verified

The equation 鈭�4d+6=12has solution set aslocalid="1645012230218" d=鈭�1.5and d=4.5and 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 −4d+6=12.

Simplify the expression for d.

鈭�4d+6鈭�6=12鈭�6鈭�4d=6鈭�4d鈭�4=6鈭�4d=鈭�1.5

03

Step-3. Formulate case 2 when −4d+6=−12.

Simplify the expression for d.

鈭�4d+6鈭�6=鈭�12鈭�6鈭�4d=鈭�18鈭�4d4=鈭�184鈭�d脳鈭�1=鈭�4.5脳鈭�1d=4.5

04

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

From case 1 and case 2, d=鈭�1.5鈥�,鈥夆赌�4.5. Plot these values on the number line.

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