Solve for x -6<4-2x<=8

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

Step 1

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

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

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

Subtract $4$ from $- 6$ .

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

Subtract $4$ from $8$ .

$- 10 < - 2 x \leq 4$

Step 2

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

$\frac{- 10}{- 2} > \frac{- 2 x}{- 2} \geq \frac{4}{- 2}$

Step 3

Divide $- 10$ by $- 2$ .

$5 > \frac{- 2 x}{- 2} \geq \frac{4}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$5 > \frac{- 2 x}{- 2} \geq \frac{4}{- 2}$

Divide $x$ by $1$ .

$5 > x \geq \frac{4}{- 2}$

Step 5

Divide $4$ by $- 2$ .

$5 > x \geq - 2$

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.

$- 2 \leq x < 5$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 2 \leq x < 5$

Interval Notation:

$[- 2, 5)$

Step 8