Solve for x -2<8-2x<=-1

$- 2 < 8 - 2 x \leq - 1$

Step 1

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.

$- 2 - 8 < - 2 x \leq - 1 - 8$

Subtract $8$ from $- 2$ .

$- 10 < - 2 x \leq - 1 - 8$

Subtract $8$ from $- 1$ .

$- 10 < - 2 x \leq - 9$

Step 2

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

$\frac{- 10}{- 2} > \frac{- 2 x}{- 2} \geq \frac{- 9}{- 2}$

Step 3

Divide $- 10$ by $- 2$ .

$5 > \frac{- 2 x}{- 2} \geq \frac{- 9}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$5 > \frac{- 2 x}{- 2} \geq \frac{- 9}{- 2}$

Divide $x$ by $1$ .

$5 > x \geq \frac{- 9}{- 2}$

Step 5

Dividing two negative values results in a positive value.

$5 > x \geq \frac{9}{2}$

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.

$\frac{9}{2} \leq x < 5$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$\frac{9}{2} \leq x < 5$

Interval Notation:

$[\frac{9}{2}, 5)$

Step 8