Trigonometry Examples

$- \frac{2}{3} x + 9 > 7$

Step 1

Simplify each term.

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Step 1.1

Combine $x$ and $\frac{2}{3}$ .

$- \frac{x \cdot 2}{3} + 9 > 7$

Step 1.2

Move $2$ to the left of $x$ .

$- \frac{2 x}{3} + 9 > 7$

Step 2

Move all terms not containing $x$ to the right side of the inequality.

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Step 2.1

Subtract $9$ from both sides of the inequality.

$- \frac{2 x}{3} > 7 - 9$

Step 2.2

Subtract $9$ from $7$ .

$- \frac{2 x}{3} > - 2$

Step 3

Divide each term in $- \frac{2 x}{3} > - 2$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- \frac{2 x}{3} > - 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{2 x}{3}}{- 1} < \frac{- 2}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{2 x}{3}}{1} < \frac{- 2}{- 1}$

Step 3.2.2

Divide $\frac{2 x}{3}$ by $1$ .

$\frac{2 x}{3} < \frac{- 2}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 2$ by $- 1$ .

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

Step 4

Multiply both sides by $3$ .

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

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1

Cancel the common factor.

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

Step 5.1.1.2

Rewrite the expression.

$2 x < 2 \cdot 3$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $2$ by $3$ .

$2 x < 6$

Step 6

Divide each term in $2 x < 6$ by $2$ and simplify.

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Step 6.1

Divide each term in $2 x < 6$ by $2$ .

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

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $2$ .

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Step 6.2.1.1

Cancel the common factor.

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

Step 6.2.1.2

Divide $x$ by $1$ .

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

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $6$ by $2$ .

$x < 3$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x < 3$

Interval Notation:

$(- \infty, 3)$