Solve for x -10<=2x-4<8

$- 10 \leq 2 x - 4 < 8$

Step 1

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.

$- 10 + 4 \leq 2 x < 8 + 4$

Add $- 10$ and $4$ .

$- 6 \leq 2 x < 8 + 4$

Add $8$ and $4$ .

$- 6 \leq 2 x < 12$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 6}{2} \leq \frac{2 x}{2} < \frac{12}{2}$

Step 3

Divide $- 6$ by $2$ .

$- 3 \leq \frac{2 x}{2} < \frac{12}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 3 \leq \frac{2 x}{2} < \frac{12}{2}$

Divide $x$ by $1$ .

$- 3 \leq x < \frac{12}{2}$

Step 5

Divide $12$ by $2$ .

$- 3 \leq x < 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 3 \leq x < 6$

Interval Notation:

$[- 3, 6)$

Step 7