Solve the Inequality for k -6<=-2k+8<=2

$- 6 \leq - 2 k + 8 \leq 2$

Step 1

Move all terms not containing $k$ 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.

$- 6 - 8 \leq - 2 k \leq 2 - 8$

Subtract $8$ from $- 6$ .

$- 14 \leq - 2 k \leq 2 - 8$

Subtract $8$ from $2$ .

$- 14 \leq - 2 k \leq - 6$

Step 2

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

$\frac{- 14}{- 2} \geq \frac{- 2 k}{- 2} \geq \frac{- 6}{- 2}$

Step 3

Divide $- 14$ by $- 2$ .

$7 \geq \frac{- 2 k}{- 2} \geq \frac{- 6}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$7 \geq \frac{- 2 k}{- 2} \geq \frac{- 6}{- 2}$

Divide $k$ by $1$ .

$7 \geq k \geq \frac{- 6}{- 2}$

Step 5

Divide $- 6$ by $- 2$ .

$7 \geq k \geq 3$

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.

$3 \leq k \leq 7$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$3 \leq k \leq 7$

Interval Notation:

$[3, 7]$

Step 8