Algebra Examples

$- 3 < \frac{4 x - 6}{5} < 0$

Step 1

Factor $2$ out of $4 x - 6$ .

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Step 1.1

Factor $2$ out of $4 x$ .

$- 3 < \frac{2 (2 x) - 6}{5} < 0$

Step 1.2

Factor $2$ out of $- 6$ .

$- 3 < \frac{2 (2 x) + 2 (- 3)}{5} < 0$

Step 1.3

Factor $2$ out of $2 (2 x) + 2 (- 3)$ .

$- 3 < \frac{2 (2 x - 3)}{5} < 0$

Step 2

Multiply each term in the inequality by $5$ .

$- 3 \cdot 5 < \frac{2 (2 x - 3)}{5} \cdot 5 < 0 \cdot 5$

Step 3

Multiply $- 3$ by $5$ .

$- 15 < \frac{2 (2 x - 3)}{5} \cdot 5 < 0 \cdot 5$

Step 4

Cancel the common factor of $5$ .

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Step 4.1

Cancel the common factor.

$- 15 < \frac{2 (2 x - 3)}{5} \cdot 5 < 0 \cdot 5$

Step 4.2

Rewrite the expression.

$- 15 < 2 (2 x - 3) < 0 \cdot 5$

Step 5

Apply the distributive property.

$- 15 < 2 (2 x) + 2 \cdot - 3 < 0 \cdot 5$

Step 6

Multiply.

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Step 6.1

Multiply $2$ by $2$ .

$- 15 < 4 x + 2 \cdot - 3 < 0 \cdot 5$

Step 6.2

Multiply $2$ by $- 3$ .

$- 15 < 4 x - 6 < 0 \cdot 5$

Step 7

Multiply $0$ by $5$ .

$- 15 < 4 x - 6 < 0$

Step 8

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

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Step 8.1

Add $6$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 15 + 6 < 4 x < 0 + 6$

Step 8.2

Add $- 15$ and $6$ .

$- 9 < 4 x < 0 + 6$

Step 8.3

Add $0$ and $6$ .

$- 9 < 4 x < 6$

Step 9

Divide each term in the inequality by $4$ .

$\frac{- 9}{4} < \frac{4 x}{4} < \frac{6}{4}$

Step 10

Move the negative in front of the fraction.

$- \frac{9}{4} < \frac{4 x}{4} < \frac{6}{4}$

Step 11

Cancel the common factor of $4$ .

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Step 11.1

Cancel the common factor.

$- \frac{9}{4} < \frac{4 x}{4} < \frac{6}{4}$

Step 11.2

Divide $x$ by $1$ .

$- \frac{9}{4} < x < \frac{6}{4}$

Step 12

Cancel the common factor of $6$ and $4$ .

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Step 12.1

Factor $2$ out of $6$ .

$- \frac{9}{4} < x < \frac{2 (3)}{4}$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $2$ out of $4$ .

$- \frac{9}{4} < x < \frac{2 \cdot 3}{2 \cdot 2}$

Step 12.2.2

Cancel the common factor.

$- \frac{9}{4} < x < \frac{2 \cdot 3}{2 \cdot 2}$

Step 12.2.3

Rewrite the expression.

$- \frac{9}{4} < x < \frac{3}{2}$

Step 13

Convert the inequality to interval notation.

$(- \frac{9}{4}, \frac{3}{2})$

Step 14