Solve for m -1<4m+7<=11

$- 1 < 4 m + 7 \leq 11$

Step 1

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

Subtract $7$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 1 - 7 < 4 m \leq 11 - 7$

Subtract $7$ from $- 1$ .

$- 8 < 4 m \leq 11 - 7$

Subtract $7$ from $11$ .

$- 8 < 4 m \leq 4$

Step 2

Divide each term in the inequality by $4$ .

$\frac{- 8}{4} < \frac{4 m}{4} \leq \frac{4}{4}$

Step 3

Divide $- 8$ by $4$ .

$- 2 < \frac{4 m}{4} \leq \frac{4}{4}$

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

$- 2 < \frac{4 m}{4} \leq \frac{4}{4}$

Divide $m$ by $1$ .

$- 2 < m \leq \frac{4}{4}$

Step 5

Divide $4$ by $4$ .

$- 2 < m \leq 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 2 < m \leq 1$

Interval Notation:

$(- 2, 1]$

Step 7