Trigonometry Examples

$\frac{x}{4} + \frac{3 x}{8} > 10$

Step 1

Simplify $\frac{x}{4} + \frac{3 x}{8}$ .

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Step 1.1

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{4} \cdot \frac{2}{2} + \frac{3 x}{8} > 10$

Step 1.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{x}{4}$ by $\frac{2}{2}$ .

$\frac{x \cdot 2}{4 \cdot 2} + \frac{3 x}{8} > 10$

Step 1.2.2

Multiply $4$ by $2$ .

$\frac{x \cdot 2}{8} + \frac{3 x}{8} > 10$

Step 1.3

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 3 x}{8} > 10$

Step 1.4

Simplify the numerator.

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Step 1.4.1

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

$\frac{2 \cdot x + 3 x}{8} > 10$

Step 1.4.2

Add $2 x$ and $3 x$ .

$\frac{5 x}{8} > 10$

Step 2

Multiply both sides by $8$ .

$\frac{5 x}{8} \cdot 8 > 10 \cdot 8$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $8$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{5 x}{8} \cdot 8 > 10 \cdot 8$

Step 3.1.1.2

Rewrite the expression.

$5 x > 10 \cdot 8$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $10$ by $8$ .

$5 x > 80$

Step 4

Divide each term in $5 x > 80$ by $5$ and simplify.

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Step 4.1

Divide each term in $5 x > 80$ by $5$ .

$\frac{5 x}{5} > \frac{80}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 x}{5} > \frac{80}{5}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x > \frac{80}{5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $80$ by $5$ .

$x > 16$

Step 5

Convert the inequality to interval notation.

$(16, \infty)$

Step 6