Solve for m -5<=3m+1<4

$- 5 \leq 3 m + 1 < 4$

Step 1

Move all terms not containing $m$ 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.

$- 5 - 1 \leq 3 m < 4 - 1$

Subtract $1$ from $- 5$ .

$- 6 \leq 3 m < 4 - 1$

Subtract $1$ from $4$ .

$- 6 \leq 3 m < 3$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 6}{3} \leq \frac{3 m}{3} < \frac{3}{3}$

Step 3

Divide $- 6$ by $3$ .

$- 2 \leq \frac{3 m}{3} < \frac{3}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 2 \leq \frac{3 m}{3} < \frac{3}{3}$

Divide $m$ by $1$ .

$- 2 \leq m < \frac{3}{3}$

Step 5

Divide $3$ by $3$ .

$- 2 \leq m < 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 2 \leq m < 1$

Interval Notation:

$[- 2, 1)$

Step 7