Solve for x -6<6-2x<=10

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

Step 1

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

Subtract $6$ from each section of the inequality because it does not contain the variable we are trying to solve for.

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

Subtract $6$ from $- 6$ .

$- 12 < - 2 x \leq 10 - 6$

Subtract $6$ from $10$ .

$- 12 < - 2 x \leq 4$

Step 2

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

$\frac{- 12}{- 2} > \frac{- 2 x}{- 2} \geq \frac{4}{- 2}$

Step 3

Divide $- 12$ by $- 2$ .

$6 > \frac{- 2 x}{- 2} \geq \frac{4}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$6 > \frac{- 2 x}{- 2} \geq \frac{4}{- 2}$

Divide $x$ by $1$ .

$6 > x \geq \frac{4}{- 2}$

Step 5

Divide $4$ by $- 2$ .

$6 > x \geq - 2$

Step 6

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

$- 2 \leq x < 6$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 2 \leq x < 6$

Interval Notation:

$[- 2, 6)$

Step 8