Solve the Inequality for x 6>=8-2x>=-2

$6 \geq 8 - 2 x \geq - 2$

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

Subtract $8$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$6 - 8 \geq - 2 x \geq - 2 - 8$

Subtract $8$ from $6$ .

$- 2 \geq - 2 x \geq - 2 - 8$

Subtract $8$ from $- 2$ .

$- 2 \geq - 2 x \geq - 10$

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

$\frac{- 2}{- 2} \leq \frac{- 2 x}{- 2} \leq \frac{- 10}{- 2}$

Divide $- 2$ by $- 2$ .

$1 \leq \frac{- 2 x}{- 2} \leq \frac{- 10}{- 2}$

Cancel the common factor of $- 2$ .

Cancel the common factor.

$1 \leq \frac{- 2 x}{- 2} \leq \frac{- 10}{- 2}$

Divide $x$ by $1$ .

$1 \leq x \leq \frac{- 10}{- 2}$

Divide $- 10$ by $- 2$ .

$1 \leq x \leq 5$

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x \leq 5$

Interval Notation:

$[1, 5]$