Chapter 1.4, Problem 46E

To determine

whether the friend is correct

Answer to Problem 46E

Friend is not correct.

Explanation of Solution

Given:

Absolute value equation $\left|3x+8\right|-9=-5$

Calculation:

1 Although the constant on the right side is negative does not mean there is no solution. Because the negative nine is outside the absolute value, the solution can exist.
2 $\left|3x+8\right|-9=-5$		Example
3 $\left|3x+8\right|=4$		Isolate the absolute value
4 $\left(3x+8\right)=4$	$-\left(3x+8\right)=4$	Make one part of the absolute value positive and the other negative
5 $3x=-4$	$-3x=12$	Solve for the x values
6 $x=-\frac{4}{3}$	$x=-4$	$2$ solutions for $x$

RESULT No, Friend is not correct.

Conclusion:

Friend is not correct.