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