Solve the Inequality for x -5<=3-2x<11

$- 5 \leq 3 - 2 x < 11$

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

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 - 3 \leq - 2 x < 11 - 3$

Subtract $3$ from $- 5$ .

$- 8 \leq - 2 x < 11 - 3$

Subtract $3$ from $11$ .

$- 8 \leq - 2 x < 8$

Divide each term in the inequality by $- 2$ .

$\frac{- 8}{- 2} \geq \frac{- 2 x}{- 2} > \frac{8}{- 2}$

Divide $- 8$ by $- 2$ .

$4 \geq \frac{- 2 x}{- 2} > \frac{8}{- 2}$

Cancel the common factor of $- 2$ .

Cancel the common factor.

$4 \geq \frac{- 2 x}{- 2} > \frac{8}{- 2}$

Divide $x$ by $1$ .

$4 \geq x > \frac{8}{- 2}$

Divide $8$ by $- 2$ .

$4 \geq x > - 4$

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 4 < x \leq 4$

The result can be shown in multiple forms.

Inequality Form:

$- 4 < x \leq 4$

Interval Notation:

$(- 4, 4]$