Question

$|3x + 5| = 5x + 11$

Explanation:

Step1: Consider two cases for absolute - value

Case 1: $3x + 5\geq0$, then $|3x + 5|=3x + 5$. The equation becomes $3x + 5=5x + 11$.
Subtract $3x$ from both sides: $5 = 2x+11$.
Subtract 11 from both sides: $2x=5 - 11=-6$.
Divide both sides by 2: $x=-3$. But when $x = - 3$, $3x+5=3\times(-3)+5=-9 + 5=-4<0$, so this solution is not valid for this case.
Case 2: $3x + 5<0$, then $|3x + 5|=-(3x + 5)$. The equation becomes $-(3x + 5)=5x + 11$.
Expand the left - hand side: $-3x-5 = 5x + 11$.
Add $3x$ to both sides: $-5=8x + 11$.
Subtract 11 from both sides: $8x=-5 - 11=-16$.
Divide both sides by 8: $x=-2$. When $x=-2$, $3x + 5=3\times(-2)+5=-6 + 5=-1<0$, so this solution is valid.

Answer:

$x=-2$