\(\displaystyle | x - 10| = 100 \)

\(\displaystyle (x - 10) = 100 \)

\(\displaystyle x - 10 = 100 \)

\(\displaystyle x - 10 + 10 = 100 + 10\)

\(\displaystyle x = 110\)

Check

\(\displaystyle |(110) - 10| = 100\)

\(\displaystyle |100| = 100\)

Negative side:

\(\displaystyle | x - 10| = 100 \)

\(\displaystyle -(x - 10) = 100 \)

\(\displaystyle -x + 10 = 100 \)

\(\displaystyle -x + 10 - 10 = 100 - 10 \)

\(\displaystyle -x = 90\)

\(\displaystyle \dfrac{x}{-1} = \dfrac{90}{-1}\)

\(\displaystyle x = -90\)

Check

\(\displaystyle |(-90) - 10| = 100\)

\(\displaystyle |-100| = 100\)

Two solutions of \(\displaystyle 110,-90\)