Precalculus Examples

$- 6 < \frac{2 x - 8}{3} < 0$

Step 1

Factor $2$ out of $2 x - 8$ .

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Step 1.1

Factor $2$ out of $2 x$ .

$- 6 < \frac{2 (x) - 8}{3} < 0$

Step 1.2

Factor $2$ out of $- 8$ .

$- 6 < \frac{2 x + 2 \cdot - 4}{3} < 0$

Step 1.3

Factor $2$ out of $2 x + 2 \cdot - 4$ .

$- 6 < \frac{2 (x - 4)}{3} < 0$

Step 2

Multiply each term in the inequality by $3$ .

$- 6 \cdot 3 < \frac{2 (x - 4)}{3} \cdot 3 < 0 \cdot 3$

Step 3

Multiply $- 6$ by $3$ .

$- 18 < \frac{2 (x - 4)}{3} \cdot 3 < 0 \cdot 3$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

$- 18 < \frac{2 (x - 4)}{3} \cdot 3 < 0 \cdot 3$

Step 4.2

Rewrite the expression.

$- 18 < 2 (x - 4) < 0 \cdot 3$

Step 5

Apply the distributive property.

$- 18 < 2 x + 2 \cdot - 4 < 0 \cdot 3$

Step 6

Multiply $2$ by $- 4$ .

$- 18 < 2 x - 8 < 0 \cdot 3$

Step 7

Multiply $0$ by $3$ .

$- 18 < 2 x - 8 < 0$

Step 8

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

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Step 8.1

Add $8$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 18 + 8 < 2 x < 0 + 8$

Step 8.2

Add $- 18$ and $8$ .

$- 10 < 2 x < 0 + 8$

Step 8.3

Add $0$ and $8$ .

$- 10 < 2 x < 8$

Step 9

Divide each term in the inequality by $2$ .

$\frac{- 10}{2} < \frac{2 x}{2} < \frac{8}{2}$

Step 10

Divide $- 10$ by $2$ .

$- 5 < \frac{2 x}{2} < \frac{8}{2}$

Step 11

Cancel the common factor of $2$ .

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Step 11.1

Cancel the common factor.

$- 5 < \frac{2 x}{2} < \frac{8}{2}$

Step 11.2

Divide $x$ by $1$ .

$- 5 < x < \frac{8}{2}$

Step 12

Divide $8$ by $2$ .

$- 5 < x < 4$

Step 13

Convert the inequality to interval notation.

$(- 5, 4)$

Step 14