Solve for x -5<=3x+1<=16

$- 5 \leq 3 x + 1 \leq 16$

Step 1

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

Subtract $1$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 - 1 \leq 3 x \leq 16 - 1$

Subtract $1$ from $- 5$ .

$- 6 \leq 3 x \leq 16 - 1$

Subtract $1$ from $16$ .

$- 6 \leq 3 x \leq 15$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 6}{3} \leq \frac{3 x}{3} \leq \frac{15}{3}$

Step 3

Divide $- 6$ by $3$ .

$- 2 \leq \frac{3 x}{3} \leq \frac{15}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 2 \leq \frac{3 x}{3} \leq \frac{15}{3}$

Divide $x$ by $1$ .

$- 2 \leq x \leq \frac{15}{3}$

Step 5

Divide $15$ by $3$ .

$- 2 \leq x \leq 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 2 \leq x \leq 5$

Interval Notation:

$[- 2, 5]$

Step 7