# Evaluate: |x+3| <= 2

## Expression: $|x+3| \leq 2$

Adding is the same as subtracting the opposite

$|x-\left( -3 \right)| \leq 2$

The inequality represents all real numbers $x$ with distance from $-3$ that is less than or equal to $2$, so $|x-\left( -3 \right)| \leq 2$ means the same as the compound inequality $-2 \leq x-\left( -3 \right) \leq 2$

$-2 \leq x-\left( -3 \right) \leq 2$

When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses

$-2 \leq x+3 \leq 2$

Subtract $3$ from each part of the inequality

\begin{align*}&-5 \leq x \leq -1 \\&\begin{array} { l }x \in \left[ -5, -1\right]\end{array}\end{align*}

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