Solve for a -5<=4a-1<11

$- 5 \leq 4 a - 1 < 11$

Step 1

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

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

$- 5 + 1 \leq 4 a < 11 + 1$

Add $- 5$ and $1$ .

$- 4 \leq 4 a < 11 + 1$

Add $11$ and $1$ .

$- 4 \leq 4 a < 12$

Step 2

Divide each term in the inequality by $4$ .

$\frac{- 4}{4} \leq \frac{4 a}{4} < \frac{12}{4}$

Step 3

Divide $- 4$ by $4$ .

$- 1 \leq \frac{4 a}{4} < \frac{12}{4}$

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

$- 1 \leq \frac{4 a}{4} < \frac{12}{4}$

Divide $a$ by $1$ .

$- 1 \leq a < \frac{12}{4}$

Step 5

Divide $12$ by $4$ .

$- 1 \leq a < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 1 \leq a < 3$

Interval Notation:

$[- 1, 3)$

Step 7