Trigonometry Examples

$\frac{2}{9} x - 1 < \frac{27}{2}$

Step 1

Combine $\frac{2}{9}$ and $x$ .

$\frac{2 x}{9} - 1 < \frac{27}{2}$

Step 2

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

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Step 2.1

Add $1$ to both sides of the inequality.

$\frac{2 x}{9} < \frac{27}{2} + 1$

Step 2.2

Write $1$ as a fraction with a common denominator.

$\frac{2 x}{9} < \frac{27}{2} + \frac{2}{2}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{2 x}{9} < \frac{27 + 2}{2}$

Step 2.4

Add $27$ and $2$ .

$\frac{2 x}{9} < \frac{29}{2}$

Step 3

Multiply both sides by $9$ .

$\frac{2 x}{9} \cdot 9 < \frac{29}{2} \cdot 9$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $9$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{2 x}{9} \cdot 9 < \frac{29}{2} \cdot 9$

Step 4.1.1.2

Rewrite the expression.

$2 x < \frac{29}{2} \cdot 9$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{29}{2} \cdot 9$ .

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Step 4.2.1.1

Combine $\frac{29}{2}$ and $9$ .

$2 x < \frac{29 \cdot 9}{2}$

Step 4.2.1.2

Multiply $29$ by $9$ .

$2 x < \frac{261}{2}$

Step 5

Divide each term in $2 x < \frac{261}{2}$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 x < \frac{261}{2}$ by $2$ .

$\frac{2 x}{2} < \frac{\frac{261}{2}}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} < \frac{\frac{261}{2}}{2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x < \frac{\frac{261}{2}}{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$x < \frac{261}{2} \cdot \frac{1}{2}$

Step 5.3.2

Multiply $\frac{261}{2} \cdot \frac{1}{2}$ .

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Step 5.3.2.1

Multiply $\frac{261}{2}$ by $\frac{1}{2}$ .

$x < \frac{261}{2 \cdot 2}$

Step 5.3.2.2

Multiply $2$ by $2$ .

$x < \frac{261}{4}$

Step 6