\(\displaystyle | x + 5| = 15 \)

\(\displaystyle (x + 5) = 15 \)

\(\displaystyle x + 5 = 15 \)

\(\displaystyle x + 5 - 5 = 15 - 5\)

\(\displaystyle x = 10\)

Check

\(\displaystyle |(10) + 5| = 15\)

\(\displaystyle |15| = 15\)

Negative side:

\(\displaystyle | x + 5| = 15 \)

\(\displaystyle -(x + 5) = 15 \)

\(\displaystyle -x - 5 = 15 \)

\(\displaystyle -x - 5 + 5 = 15 + 5 \)

\(\displaystyle -x = 20\)

\(\displaystyle \dfrac{x}{-1} = \dfrac{20}{-1}\)

\(\displaystyle x = -20\)

Check

\(\displaystyle |(-20) + 5| = 15\)

\(\displaystyle |-15| = 15\)

Two solutions of \(\displaystyle 10, -20\)