Answer
The solutions are $c=1$ and $c=-\frac{2}{3}$.
Work Step by Step
The given equation is
$\Rightarrow |2c+8|=|10c|$
Write the two related linear equations.
$2c+8=10c$ ...... (1)
$2c+8=-10c$ ...... (2)
Solve equation (1).
$\Rightarrow 2c+8=10c$
Subtract $2c$ from each side.
$\Rightarrow 2c+8-2c=10c-2c$
Simplify.
$\Rightarrow 8=8c$
Divide each side by $8$.
$\Rightarrow \frac{8}{8}=\frac{8c}{8}$
Simplify.
$\Rightarrow 1=c$
Check : $c=1$
$\Rightarrow |2c+8|=|10c|$
$\Rightarrow |2(1)+8|=|10(1)|$
$\Rightarrow |2+8|=|10|$
$\Rightarrow |10|=|10|$
True.
Solve equation (2).
$\Rightarrow 2c+8=-10c$
Add $10c-8$ to each side.
$\Rightarrow 2c+8+10c-8=-10c+10c-8$
Simplify.
$\Rightarrow 12c=-8$
Divide each side by $12$.
$\Rightarrow \frac{12c}{12}=-\frac{8}{12}$
Simplify.
$\Rightarrow c=-\frac{2}{3}$
Check : $c=-\frac{2}{3}$
$\Rightarrow |2c+8|=|10c|$
$\Rightarrow |2(-\frac{2}{3})+8|=|10(-\frac{2}{3})|$
$\Rightarrow |-\frac{4}{3}+8|=|\frac{20}{3}|$
$\Rightarrow |\frac{-4+24}{3}|=|\frac{20}{3}|$
$\Rightarrow |\frac{20}{3}|=|\frac{20}{3}|$
True.
Hence, the solutions are $c=1$ and $c=-\frac{2}{3}$.
