Pre-Algebra Examples

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

Step 1

Multiply each term in the inequality by $3$ .

$- 5 \cdot 3 < \frac{2 x - 3}{3} \cdot 3 < 5 \cdot 3$

Step 2

Multiply $- 5$ by $3$ .

$- 15 < \frac{2 x - 3}{3} \cdot 3 < 5 \cdot 3$

Step 3

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$- 15 < \frac{2 x - 3}{3} \cdot 3 < 5 \cdot 3$

Step 3.2

Rewrite the expression.

$- 15 < 2 x - 3 < 5 \cdot 3$

Step 4

Multiply $5$ by $3$ .

$- 15 < 2 x - 3 < 15$

Step 5

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

Tap for more steps...

Step 5.1

Add $3$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 15 + 3 < 2 x < 15 + 3$

Step 5.2

Add $- 15$ and $3$ .

$- 12 < 2 x < 15 + 3$

Step 5.3

Add $15$ and $3$ .

$- 12 < 2 x < 18$

Step 6

Divide each term in the inequality by $2$ .

$\frac{- 12}{2} < \frac{2 x}{2} < \frac{18}{2}$

Step 7

Divide $- 12$ by $2$ .

$- 6 < \frac{2 x}{2} < \frac{18}{2}$

Step 8

Cancel the common factor of $2$ .

Tap for more steps...

Step 8.1

Cancel the common factor.

$- 6 < \frac{2 x}{2} < \frac{18}{2}$

Step 8.2

Divide $x$ by $1$ .

$- 6 < x < \frac{18}{2}$

Step 9

Divide $18$ by $2$ .

$- 6 < x < 9$

Step 10