Question

What is the solution of |2x + 3| = 3x + 5?

Answer 1

Answer:

$x=-\frac{8}{5}$

Step-by-step explanation:

The given absolute value equation is

$|2x+3|=3x+5$

This implies that;

$-(2x+3)=3x+5\:or\:2x+3=3x+5$

$-2x-3=3x+5\:or\:2x+3=3x+5$

Group similar terms in both equations;

$-2x-3x=5+3\:or\:2x-3x=5-3$

$-5x=8\:or\:-x=-2$

$x=-\frac{8}{5}\:or\:x=2$

CHECK

$|2(2)+3|=3(2)+5$

$|4+3|=6+5$

$7=11$.

This false. Hence  x=2 is an extraneous solution.

When $x=-\frac{8}{5}$

$|2(-\frac{8}{5})+3|=3(-\frac{8}{5})+5$

$|-\frac{16}{5}+3|=(-\frac{24}{5})+5$

$|-\frac{1}{5}|=\frac{1}{5}$

$\frac{1}{5}=\frac{1}{5}$

This statement is true

Answer 2

Answer:

The right answer is x = -8/5

Step-by-step explanation:

See the attached figure