Trigonometry Examples

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

Step 1

Factor $3$ out of $3 x - 6$ .

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Step 1.1

Factor $3$ out of $3 x$ .

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

Step 1.2

Factor $3$ out of $- 6$ .

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

Step 1.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

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

Step 2

Multiply each term in the inequality by $5$ .

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

Step 3

Multiply $- 3$ by $5$ .

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

Step 4

Cancel the common factor of $5$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Apply the distributive property.

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

Step 6

Multiply $3$ by $- 2$ .

$- 15 < 3 x - 6 < 0 \cdot 5$

Step 7

Multiply $0$ by $5$ .

$- 15 < 3 x - 6 < 0$

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.

$- 15 + 6 < 3 x < 0 + 6$

Step 8.2

Add $- 15$ and $6$ .

$- 9 < 3 x < 0 + 6$

Step 8.3

Add $0$ and $6$ .

$- 9 < 3 x < 6$

Step 9

Divide each term in the inequality by $3$ .

$\frac{- 9}{3} < \frac{3 x}{3} < \frac{6}{3}$

Step 10

Divide $- 9$ by $3$ .

$- 3 < \frac{3 x}{3} < \frac{6}{3}$

Step 11

Cancel the common factor of $3$ .

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Step 11.1

Cancel the common factor.

$- 3 < \frac{3 x}{3} < \frac{6}{3}$

Step 11.2

Divide $x$ by $1$ .

$- 3 < x < \frac{6}{3}$

Step 12

Divide $6$ by $3$ .

$- 3 < x < 2$

Step 13

Convert the inequality to interval notation.

$(- 3, 2)$

Step 14