Answer:
[tex]x=-\frac{8}{5}[/tex]
Step-by-step explanation:
The given absolute value equation is
[tex]|2x+3|=3x+5[/tex]
This implies that;
[tex]-(2x+3)=3x+5\:or\:2x+3=3x+5[/tex]
[tex]-2x-3=3x+5\:or\:2x+3=3x+5[/tex]
Group similar terms in both equations;
[tex]-2x-3x=5+3\:or\:2x-3x=5-3[/tex]
[tex]-5x=8\:or\:-x=-2[/tex]
[tex]x=-\frac{8}{5}\:or\:x=2[/tex]
CHECK
[tex]|2(2)+3|=3(2)+5[/tex]
[tex]|4+3|=6+5[/tex]
[tex]7=11[/tex].
This false. Hence x=2 is an extraneous solution.
When [tex]x=-\frac{8}{5}[/tex]
[tex]|2(-\frac{8}{5})+3|=3(-\frac{8}{5})+5[/tex]
[tex]|-\frac{16}{5}+3|=(-\frac{24}{5})+5[/tex]
[tex]|-\frac{1}{5}|=\frac{1}{5}[/tex]
[tex]\frac{1}{5}=\frac{1}{5}[/tex]
This statement is true
