∣x+5∣≤8

To solve the inequality \( |x + 5| \leq 8 \), we will break it down based on the definition of absolute value.

The inequality \( |A| \leq B \) means that \( -B \leq A \leq B \). In this case:

\[
-8 \leq x + 5 \leq 8.
\]

We will solve the two inequalities separately.

1. Solve the left inequality:

\[
-8 \leq x + 5
\]

Subtract 5 from both sides:

\[
-8 - 5 \leq x \implies -13 \leq x \implies x \geq -13.
\]

2. Solve the right inequality:

\[
x + 5 \leq 8.
\]

Subtract 5 from both sides:

\[
x \leq 8 - 5 \implies x \leq 3.
\]

Combining the results from both inequalities, we find:

\[
-13 \leq x \leq 3.
\]

Thus, the solution to the inequality \( |x + 5| \leq 8 \) is:

\[
\boxed{[-13, 3]}.
\]