Solve for x -2<=(x+9)/18<=2

$- 2 \leq \frac{x + 9}{18} \leq 2$

Step 1

Multiply each term in the inequality by $18$ .

$- 2 \cdot 18 \leq \frac{x + 9}{18} \cdot 18 \leq 2 \cdot 18$

Step 2

Multiply $- 2$ by $18$ .

$- 36 \leq \frac{x + 9}{18} \cdot 18 \leq 2 \cdot 18$

Step 3

Cancel the common factor of $18$ .

Cancel the common factor.

$- 36 \leq \frac{x + 9}{18} \cdot 18 \leq 2 \cdot 18$

Rewrite the expression.

$- 36 \leq x + 9 \leq 2 \cdot 18$

Step 4

Multiply $2$ by $18$ .

$- 36 \leq x + 9 \leq 36$

Step 5

Move all terms not containing $x$ from the center section of the inequality.

Subtract $9$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 36 - 9 \leq x \leq 36 - 9$

Subtract $9$ from $- 36$ .

$- 45 \leq x \leq 36 - 9$

Subtract $9$ from $36$ .

$- 45 \leq x \leq 27$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 45 \leq x \leq 27$

Interval Notation:

$[- 45, 27]$

Step 7