Solve for x 2<=2x-2<=-5

$2 \leq 2 x - 2 \leq - 5$

Step 1

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

Add $2$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$2 + 2 \leq 2 x \leq - 5 + 2$

Add $2$ and $2$ .

$4 \leq 2 x \leq - 5 + 2$

Add $- 5$ and $2$ .

$4 \leq 2 x \leq - 3$

Step 2

Divide each term in the inequality by $2$ .

$\frac{4}{2} \leq \frac{2 x}{2} \leq \frac{- 3}{2}$

Step 3

Divide $4$ by $2$ .

$2 \leq \frac{2 x}{2} \leq \frac{- 3}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \leq \frac{2 x}{2} \leq \frac{- 3}{2}$

Divide $x$ by $1$ .

$2 \leq x \leq \frac{- 3}{2}$

Step 5

Move the negative in front of the fraction.

$2 \leq x \leq - \frac{3}{2}$

Step 6

Since the inequality can never be true, there is no solution.

False