Solve for a -8<=3a+1<=4

$- 8 \leq 3 a + 1 \leq 4$

Step 1

Move all terms not containing $a$ 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.

$- 8 - 1 \leq 3 a \leq 4 - 1$

Subtract $1$ from $- 8$ .

$- 9 \leq 3 a \leq 4 - 1$

Subtract $1$ from $4$ .

$- 9 \leq 3 a \leq 3$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 9}{3} \leq \frac{3 a}{3} \leq \frac{3}{3}$

Step 3

Divide $- 9$ by $3$ .

$- 3 \leq \frac{3 a}{3} \leq \frac{3}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 3 \leq \frac{3 a}{3} \leq \frac{3}{3}$

Divide $a$ by $1$ .

$- 3 \leq a \leq \frac{3}{3}$

Step 5

Divide $3$ by $3$ .

$- 3 \leq a \leq 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 3 \leq a \leq 1$

Interval Notation:

$[- 3, 1]$

Step 7