Answer
The solutions are $a=\frac{5}{2}$ and $a=\frac{1}{2}$.
Work Step by Step
The given equation is
$\Rightarrow |6a-5|=4a$
Write the two related linear equations.
$6a-5=4a$ ...... (1)
$6a-5=-4a$ ...... (2)
Solve equation (1).
$\Rightarrow 6a-5=4a$
Add $5-4a$ to each side.
$\Rightarrow 6a-5+5-4a=4a+5-4a$
Simplify.
$\Rightarrow 2a=5$
Divide each side by $2$.
$\Rightarrow \frac{2a}{2}=\frac{5}{2}$
Simplify.
$\Rightarrow a=\frac{5}{2}$
Check : $a=\frac{5}{2}$
$\Rightarrow |6a-5|=4a$
$\Rightarrow |6(\frac{5}{2})-5|=4(\frac{5}{2})$
$\Rightarrow |15-5|=10$
$\Rightarrow |10|=10$
$\Rightarrow 10=10$
True.
Solve equation (2).
$\Rightarrow 6a-5=-4a$
Add $5+4a$ to each side.
$\Rightarrow 6a-5+5+4a=-4a+5+4a$
Simplify.
$\Rightarrow 10a=5$
Divide each side by $10$.
$\Rightarrow \frac{10a}{10}=\frac{5}{10}$
Simplify.
$\Rightarrow a=\frac{1}{2}$
Check : $a=\frac{1}{2}$
$\Rightarrow |6a-5|=4a$
$\Rightarrow |6(\frac{1}{2})-5|=4(\frac{1}{2})$
$\Rightarrow |3-5|=2$
$\Rightarrow |-2|=2$
$\Rightarrow 2=2$
True.
Hence, the solutions are $a=\frac{5}{2}$ and $a=\frac{1}{2}$.
