Precalculus Examples

$f (x) = \frac{5}{6} x - 25$

Step 1

Set $\frac{5}{6} x - 25$ equal to $0$ .

$\frac{5}{6} x - 25 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Combine $\frac{5}{6}$ and $x$ .

$\frac{5 x}{6} - 25 = 0$

Step 2.2

Add $25$ to both sides of the equation.

$\frac{5 x}{6} = 25$

Step 2.3

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} \cdot \frac{5 x}{6} = \frac{6}{5} \cdot 25$

Step 2.4

Simplify both sides of the equation.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Simplify $\frac{6}{5} \cdot \frac{5 x}{6}$ .

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Step 2.4.1.1.1

Cancel the common factor of $6$ .

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Step 2.4.1.1.1.1

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 x}{6} = \frac{6}{5} \cdot 25$

Step 2.4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{6}{5} \cdot 25$

Step 2.4.1.1.2

Cancel the common factor of $5$ .

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Step 2.4.1.1.2.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{6}{5} \cdot 25$

Step 2.4.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{6}{5} \cdot 25$

Step 2.4.1.1.2.3

Rewrite the expression.

$x = \frac{6}{5} \cdot 25$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Simplify $\frac{6}{5} \cdot 25$ .

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Step 2.4.2.1.1

Cancel the common factor of $5$ .

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Step 2.4.2.1.1.1

Factor $5$ out of $25$ .

$x = \frac{6}{5} \cdot (5 (5))$

Step 2.4.2.1.1.2

Cancel the common factor.

$x = \frac{6}{5} \cdot (5 \cdot 5)$

Step 2.4.2.1.1.3

Rewrite the expression.

$x = 6 \cdot 5$

Step 2.4.2.1.2

Multiply $6$ by $5$ .

$x = 30$

Step 3