Solve the Inequality for x -24<=2x-10<-6

$- 24 \leq 2 x - 10 < - 6$

Step 1

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

Add $10$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 24 + 10 \leq 2 x < - 6 + 10$

Add $- 24$ and $10$ .

$- 14 \leq 2 x < - 6 + 10$

Add $- 6$ and $10$ .

$- 14 \leq 2 x < 4$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 14}{2} \leq \frac{2 x}{2} < \frac{4}{2}$

Step 3

Divide $- 14$ by $2$ .

$- 7 \leq \frac{2 x}{2} < \frac{4}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 7 \leq \frac{2 x}{2} < \frac{4}{2}$

Divide $x$ by $1$ .

$- 7 \leq x < \frac{4}{2}$

Step 5

Divide $4$ by $2$ .

$- 7 \leq x < 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 7 \leq x < 2$

Interval Notation:

$[- 7, 2)$

Step 7