Answer
The solution is $h=\frac{1}{4}$.
Work Step by Step
The given equation is
$\Rightarrow |3h+1|=7h$
Write the two related linear equations.
$3h+1=7h$ ...... (1)
$3h+1=-7h$ ...... (2)
Solve equation (1).
$\Rightarrow 3h+1=7h$
Subtract $3h$ from each side.
$\Rightarrow 3h+1-3h=7h-3h$
Simplify.
$\Rightarrow 1=4h$
Divide each side by $4$.
$\Rightarrow \frac{1}{4}=\frac{4h}{4}$
Simplify.
$\Rightarrow \frac{1}{4}=h$
Check : $h=\frac{1}{4}$
$\Rightarrow |3h+1|=7h$
$\Rightarrow |3(\frac{1}{4})+1|=7(\frac{1}{4})$
$\Rightarrow |\frac{3}{4}+1|=\frac{7}{4}$
$\Rightarrow |\frac{3+4}{4}|=\frac{7}{4}$
$\Rightarrow |\frac{7}{4}|=\frac{7}{4}$
$\Rightarrow \frac{7}{4}=\frac{7}{4}$
True.
Solve equation (2).
$\Rightarrow 3h+1=-7h$
Subtract $3h$ from each side.
$\Rightarrow 3h+1-3h=-7h-3h$
Simplify.
$\Rightarrow 1=-10h$
Divide each side by $-10$.
$\Rightarrow -\frac{1}{10}=\frac{-10h}{-10}$
Simplify.
$\Rightarrow -\frac{1}{10}=h$
Check : $h=-\frac{1}{10}$
$\Rightarrow |3h+1|=7h$
$\Rightarrow |3(-\frac{1}{10})+1|=7(-\frac{1}{10})$
$\Rightarrow |-\frac{3}{10}+1|=-\frac{7}{10}$
$\Rightarrow |\frac{-3+10}{10}|=-\frac{7}{10}$
$\Rightarrow |\frac{7}{10}|=-\frac{7}{10}$
$\Rightarrow \frac{7}{10}=-\frac{7}{10}$
False.
Hence, the solution is $h=\frac{1}{4}$.
