Answer
$x=1$ and $x=-\frac{3}{5}$
Work Step by Step
The given equation is
$\Rightarrow -2|5x-1|-3=-11$
Add $3$ to each side.
$\Rightarrow -2|5x-1|-3+3=-11+3$
Simplify.
$\Rightarrow -2|5x-1|=-8$
Divide each side by $-2$.
$\Rightarrow \frac{-2|5x-1|}{-2}=\frac{-8}{-2}$
Simplify.
$\Rightarrow |5x-1|=4$
Write related linear equations.
$\Rightarrow 5x-1=4$ or $5x-1=−4$
Add $1$ to each side.
$\Rightarrow 5x-1+1=4+1$ or $5x-1+1=−4+1$
Simplify.
$\Rightarrow 5x=5$ or $5x=−3$
Divide each side by $5$.
$\Rightarrow \frac{5x}{5}=\frac{5}{5}$ or $\frac{5x}{5}=−\frac{3}{5}$
Simplify.
$\Rightarrow x=1$ or $x=−\frac{3}{5}$
Check $x=1$
$\Rightarrow -2|5(1)-1|-3=-11$
$\Rightarrow -2|5-1|-3=-11$
$\Rightarrow -2|4|-3=-11$
$\Rightarrow -2(4)-3=-11$
$\Rightarrow -8-3=-11$
$\Rightarrow -11=-11$
True.
Check $x=-\frac{3}{5}$
$\Rightarrow -2|5(-\frac{3}{5})-1|-3=-11$
$\Rightarrow -2|-3-1|-3=-11$
$\Rightarrow -2|-4|-3=-11$
$\Rightarrow -2(4)-3=-11$
$\Rightarrow -8-3=-11$
$\Rightarrow -11=-11$
True.
Hence, the solutions are $x=1$ and $x=-\frac{3}{5}$.
