Precalculus Examples

$- 5 \leq 2 x - 2 \leq 6$

Step 1

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

Tap for more steps...

Step 1.1

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

$- 5 + 2 \leq 2 x \leq 6 + 2$

Step 1.2

Add $- 5$ and $2$ .

$- 3 \leq 2 x \leq 6 + 2$

Step 1.3

Add $6$ and $2$ .

$- 3 \leq 2 x \leq 8$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 3}{2} \leq \frac{2 x}{2} \leq \frac{8}{2}$

Step 3

Move the negative in front of the fraction.

$- \frac{3}{2} \leq \frac{2 x}{2} \leq \frac{8}{2}$

Step 4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

$- \frac{3}{2} \leq \frac{2 x}{2} \leq \frac{8}{2}$

Step 4.2

Divide $x$ by $1$ .

$- \frac{3}{2} \leq x \leq \frac{8}{2}$

Step 5

Divide $8$ by $2$ .

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

Step 6

Convert the inequality to interval notation.

$[- \frac{3}{2}, 4]$

Step 7