Question

Solve for x.

one fifth times the absolute value of the quantity x minus 4 end quantity minus 3 equals 6

x = −49 and x = 41
x = −41 and x = 49
x = −19 and x = 11
x = −11 and x = 19

Answer 1

Well first step would be to write out the equation:
\[\large \frac{1}{5}\left| x-4 \right| -3=6\]
\[\large \frac{1}{5}\left| x-4 \right| = 9 \]

multiply by 5
\[\large 5*\frac{1}{5}\left| x-4 \right| = 9*5 \]
you get:
\[\large \left| x-4 \right| = 45 \]

now just solve these two cases:
\[\large x-4 = 45 ~and ~ x-4=-45 \]