Answer
$w=\frac{25}{4}$.
Work Step by Step
The given equation is
$\Rightarrow 6=\frac{1}{5}w+\frac{7}{5}w-4$
Use distributive property.
$\Rightarrow 6=w(\frac{1}{5}+\frac{7}{5})-4$
Add $4$ to each side.
$\Rightarrow 6+4=w(\frac{1}{5}+\frac{7}{5})-4+4$
Combine like terms.
$\Rightarrow 10=\frac{8}{5}w$
Multiply each side by $\frac{5}{8}$.
$\Rightarrow \frac{5}{8}\cdot 10=\frac{5}{8}\cdot \frac{8}{5}w$
Simplify.
$\Rightarrow \frac{25}{4}=w$
Check:-
$\Rightarrow 6=\frac{1}{5}\cdot \frac{25}{4}+\frac{7}{5}\cdot \frac{25}{4}-4$
$\Rightarrow 6=\frac{5}{4}+ \frac{35}{4}-4$
$\Rightarrow 6=\frac{40}{4}-4$
$\Rightarrow 6=10-4$
$\Rightarrow 6=6$
True.
Hence, the solution is $w=\frac{25}{4}$.
