Solve for x -2<=-2x+6<12

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

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.

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

Subtract $6$ from $- 2$ .

$- 8 \leq - 2 x < 12 - 6$

Subtract $6$ from $12$ .

$- 8 \leq - 2 x < 6$

Step 2

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

$\frac{- 8}{- 2} \geq \frac{- 2 x}{- 2} > \frac{6}{- 2}$

Step 3

Divide $- 8$ by $- 2$ .

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

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 5

Divide $6$ by $- 2$ .

$4 \geq x > - 3$

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.

$- 3 < x \leq 4$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 3 < x \leq 4$

Interval Notation:

$(- 3, 4]$

Step 8