Question

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Which of the following are solutions to ? Check all that apply.

Answer 1

ANSWER

$x = \frac{9}{2}$

EXPLANATION

The given absolute value equation is:

$|x + 4| = 3x - 5$

This implies that, either

$x + 4= 3x - 5$

$x - 3x = - 5 - 4$

$- 2x = - 9$

$x = \frac{9}{2}$

Check for extraneous solution.

$| \frac{9}{2} + 4| = \frac{27}{2} - 5$

$\frac{17}{2} = \frac{17}{2}$

This is the real solution.

Or

$- (x + 4)= 3x - 5$

This implies that:

$x + 4= - 3x + 5$

Group similar terms:

$x + 3x= 5 - 4$

$4x = 1$

$x = \frac{1}{4}$

Check for extraneous solution

$| \frac{1}{4} + 4| \ne \frac{3}{4} - 5$

This is an extraneous solution.