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

$4 \leq 8 - 2 x < 6$

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.

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

Subtract $8$ from $4$ .

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

Subtract $8$ from $6$ .

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

Step 2

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

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

Step 3

Divide $- 4$ by $- 2$ .

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

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 5

Divide $- 2$ by $- 2$ .

$2 \geq x > 1$

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.

$1 < x \leq 2$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$1 < x \leq 2$

Interval Notation:

$(1, 2]$

Step 8