Question

Solve the following inequality algebraically.
5, vertical bar, x, plus, 2, vertical bar, minus, 2, is less than or equal to, 18
5∣x+2∣−2≤18

Answer 1

To solve the inequality \( 5|x + 2| - 2 \leq 18 \), we will follow these steps:

1. **Isolate the absolute value**. Start by adding 2 to both sides of the inequality:

\[
5|x + 2| \leq 20
\]

2. **Divide by 5**. Next, divide both sides by 5:

\[
|x + 2| \leq 4
\]

3. **Remove the absolute value**. The inequality \( |x + 2| \leq 4 \) implies that:

\[
-4 \leq x + 2 \leq 4
\]

4. **Solve the compound inequality**. We can split this into two inequalities:

- From \( -4 \leq x + 2 \):
\[
x + 2 \geq -4 \implies x \geq -4 - 2 \implies x \geq -6
\]

- From \( x + 2 \leq 4 \):
\[
x + 2 \leq 4 \implies x \leq 4 - 2 \implies x \leq 2
\]

5. **Combine the results**. The two inequalities together give:

\[
-6 \leq x \leq 2
\]

Thus, the solution to the inequality \( 5|x + 2| - 2 \leq 18 \) is

\[
\boxed{[-6, 2]}
\]