Solve the Inequality for x -8<=2x-4<4

$- 8 \leq 2 x - 4 < 4$

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

Add $4$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 8 + 4 \leq 2 x < 4 + 4$

Add $- 8$ and $4$ .

$- 4 \leq 2 x < 4 + 4$

Add $4$ and $4$ .

$- 4 \leq 2 x < 8$

Divide each term in the inequality by $2$ .

$\frac{- 4}{2} \leq \frac{2 x}{2} < \frac{8}{2}$

Divide $- 4$ by $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $8$ by $2$ .

$- 2 \leq x < 4$

The result can be shown in multiple forms.

Inequality Form:

$- 2 \leq x < 4$

Interval Notation:

$[- 2, 4)$