Solve the Inequality for x -1<=2x+5<=4

$- 1 \leq 2 x + 5 \leq 4$

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

Subtract $5$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 1 - 5 \leq 2 x \leq 4 - 5$

Subtract $5$ from $- 1$ .

$- 6 \leq 2 x \leq 4 - 5$

Subtract $5$ from $4$ .

$- 6 \leq 2 x \leq - 1$

Divide each term in the inequality by $2$ .

$\frac{- 6}{2} \leq \frac{2 x}{2} \leq \frac{- 1}{2}$

Divide $- 6$ by $2$ .

$- 3 \leq \frac{2 x}{2} \leq \frac{- 1}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 3 \leq \frac{2 x}{2} \leq \frac{- 1}{2}$

Divide $x$ by $1$ .

$- 3 \leq x \leq \frac{- 1}{2}$

Move the negative in front of the fraction.

$- 3 \leq x \leq - \frac{1}{2}$

The result can be shown in multiple forms.

Inequality Form:

$- 3 \leq x \leq - \frac{1}{2}$

Interval Notation:

$[- 3, - \frac{1}{2}]$