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

$- 6 \leq - 2 x + 4 \leq 2$

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.

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

Subtract $4$ from $- 6$ .

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

Subtract $4$ from $2$ .

$- 10 \leq - 2 x \leq - 2$

Step 2

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

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

Step 3

Divide $- 10$ by $- 2$ .

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

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 5

Divide $- 2$ by $- 2$ .

$5 \geq x \geq 1$

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.

$1 \leq x \leq 5$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x \leq 5$

Interval Notation:

$[1, 5]$

Step 8