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

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

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.

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

Subtract $5$ from $- 3$ .

$- 8 \leq 2 x < 5 - 5$

Subtract $5$ from $5$ .

$- 8 \leq 2 x < 0$

Divide each term in the inequality by $2$ .

$\frac{- 8}{2} \leq \frac{2 x}{2} < \frac{0}{2}$

Divide $- 8$ by $2$ .

$- 4 \leq \frac{2 x}{2} < \frac{0}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 4 \leq \frac{2 x}{2} < \frac{0}{2}$

Divide $x$ by $1$ .

$- 4 \leq x < \frac{0}{2}$

Divide $0$ by $2$ .

$- 4 \leq x < 0$

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq x < 0$

Interval Notation:

$[- 4, 0)$