Precalculus Examples

$- 5 \leq 2 x - 2 \leq 8$

Step 1

Solve $- 5 \leq 2 x - 2$ for $x$ .

Tap for more steps...

Step 1.1

Rewrite so $x$ is on the left side of the inequality.

$2 x - 2 \geq - 5$

Step 1.2

Move all terms not containing $x$ to the right side of the inequality.

Tap for more steps...

Step 1.2.1

Add $2$ to both sides of the inequality.

$2 x \geq - 5 + 2$

Step 1.2.2

Add $- 5$ and $2$ .

$2 x \geq - 3$

Step 1.3

Divide each term in $2 x \geq - 3$ by $2$ and simplify.

Tap for more steps...

Step 1.3.1

Divide each term in $2 x \geq - 3$ by $2$ .

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

Step 1.3.2

Simplify the left side.

Tap for more steps...

Step 1.3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.2.1.1

Cancel the common factor.

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

Step 1.3.2.1.2

Divide $x$ by $1$ .

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

Step 1.3.3

Simplify the right side.

Tap for more steps...

Step 1.3.3.1

Move the negative in front of the fraction.

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

Step 2

Solve $2 x - 2 \leq 8$ for $x$ .

Tap for more steps...

Step 2.1

Move all terms not containing $x$ to the right side of the inequality.

Tap for more steps...

Step 2.1.1

Add $2$ to both sides of the inequality.

$2 x \leq 8 + 2$

Step 2.1.2

Add $8$ and $2$ .

$2 x \leq 10$

Step 2.2

Divide each term in $2 x \leq 10$ by $2$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $2 x \leq 10$ by $2$ .

$\frac{2 x}{2} \leq \frac{10}{2}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{10}{2}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{10}{2}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Divide $10$ by $2$ .

$x \leq 5$

Step 3

Find the intersection of $x \geq - \frac{3}{2}$ and $x \leq 5$ .

$- \frac{3}{2} \leq x \leq 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- \frac{3}{2} \leq x \leq 5$

Interval Notation:

$[- \frac{3}{2}, 5]$

Step 5