Question

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

x = 2
x=8/5
x=1/5 or x=7
x=8/5 or x=2

Answer 1

The right answer is x = -8/5

Explanation:

See the attached figure

Answer 2

`x=-(8)/(5)`

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=-(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=-(8)/(5)`

`|2(-(8)/(5))+3|=3(-(8)/(5))+5`

`|-(16)/(5)+3|=(-(24)/(5))+5`

`|-(1)/(5)|=(1)/(5)`

`(1)/(5)=(1)/(5)`

This statement is true