Precalculus Examples

$\frac{\sin (30)}{x} = \frac{\sin (85)}{7}$

Step 1

Factor each term.

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Step 1.1

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\frac{\frac{1}{2}}{x} = \frac{\sin (85)}{7}$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} \cdot \frac{1}{x} = \frac{\sin (85)}{7}$

Step 1.3

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

$\frac{1}{2 x} = \frac{\sin (85)}{7}$

Step 1.4

Evaluate $\sin (85)$ .

$\frac{1}{2 x} = \frac{0.99619469}{7}$

Step 1.5

Divide $0.99619469$ by $7$ .

$\frac{1}{2 x} = 0.14231352$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$2 x, 1$

Step 2.2

The LCM of one and any expression is the expression.

$2 x$

Step 3

Multiply each term in $\frac{1}{2 x} = 0.14231352$ by $2 x$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{1}{2 x} = 0.14231352$ by $2 x$ .

$\frac{1}{2 x} (2 x) = 0.14231352 (2 x)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$2 \frac{1}{2 x} x = 0.14231352 (2 x)$

Step 3.2.2

Cancel the common factor of $2$ .

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Step 3.2.2.1

Factor $2$ out of $2 x$ .

$2 \frac{1}{2 (x)} x = 0.14231352 (2 x)$

Step 3.2.2.2

Cancel the common factor.

$2 \frac{1}{2 x} x = 0.14231352 (2 x)$

Step 3.2.2.3

Rewrite the expression.

$\frac{1}{x} x = 0.14231352 (2 x)$

Step 3.2.3

Cancel the common factor of $x$ .

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Step 3.2.3.1

Cancel the common factor.

$\frac{1}{x} x = 0.14231352 (2 x)$

Step 3.2.3.2

Rewrite the expression.

$1 = 0.14231352 (2 x)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $2$ by $0.14231352$ .

$1 = 0.28462705 x$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $0.28462705 x = 1$ .

$0.28462705 x = 1$

Step 4.2

Divide each term in $0.28462705 x = 1$ by $0.28462705$ and simplify.

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Step 4.2.1

Divide each term in $0.28462705 x = 1$ by $0.28462705$ .

$\frac{0.28462705 x}{0.28462705} = \frac{1}{0.28462705}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $0.28462705$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{0.28462705 x}{0.28462705} = \frac{1}{0.28462705}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{0.28462705}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $1$ by $0.28462705$ .

$x = 3.51336943$