Precalculus Examples

$x - \frac{1}{4} x - \frac{1}{3} x - 5 = 0$

Step 1

Simplify $x - \frac{1}{4} x - \frac{1}{3} x - 5$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $x$ and $\frac{1}{4}$ .

$x - \frac{x}{4} - \frac{1}{3} x - 5 = 0$

Step 1.1.2

Combine $x$ and $\frac{1}{3}$ .

$x - \frac{x}{4} - \frac{x}{3} - 5 = 0$

Step 1.2

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

$x \cdot \frac{4}{4} - \frac{x}{4} - \frac{x}{3} - 5 = 0$

Step 1.3

Combine $x$ and $\frac{4}{4}$ .

$\frac{x \cdot 4}{4} - \frac{x}{4} - \frac{x}{3} - 5 = 0$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - x}{4} - \frac{x}{3} - 5 = 0$

Step 1.5

Subtract $x$ from $x \cdot 4$ .

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Step 1.5.1

Reorder $x$ and $4$ .

$\frac{4 \cdot x - x}{4} - \frac{x}{3} - 5 = 0$

Step 1.5.2

Subtract $x$ from $4 \cdot x$ .

$\frac{3 \cdot x}{4} - \frac{x}{3} - 5 = 0$

Step 1.6

To write $\frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 x}{4} \cdot \frac{3}{3} - \frac{x}{3} - 5 = 0$

Step 1.7

To write $- \frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 x}{4} \cdot \frac{3}{3} - \frac{x}{3} \cdot \frac{4}{4} - 5 = 0$

Step 1.8

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.8.1

Multiply $\frac{3 x}{4}$ by $\frac{3}{3}$ .

$\frac{3 x \cdot 3}{4 \cdot 3} - \frac{x}{3} \cdot \frac{4}{4} - 5 = 0$

Step 1.8.2

Multiply $4$ by $3$ .

$\frac{3 x \cdot 3}{12} - \frac{x}{3} \cdot \frac{4}{4} - 5 = 0$

Step 1.8.3

Multiply $\frac{x}{3}$ by $\frac{4}{4}$ .

$\frac{3 x \cdot 3}{12} - \frac{x \cdot 4}{3 \cdot 4} - 5 = 0$

Step 1.8.4

Multiply $3$ by $4$ .

$\frac{3 x \cdot 3}{12} - \frac{x \cdot 4}{12} - 5 = 0$

Step 1.9

Combine the numerators over the common denominator.

$\frac{3 x \cdot 3 - x \cdot 4}{12} - 5 = 0$

Step 1.10

Simplify each term.

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Step 1.10.1

Simplify the numerator.

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Step 1.10.1.1

Factor $x$ out of $3 x \cdot 3 - x \cdot 4$ .

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Step 1.10.1.1.1

Factor $x$ out of $3 x \cdot 3$ .

$\frac{x (3 \cdot 3) - x \cdot 4}{12} - 5 = 0$

Step 1.10.1.1.2

Factor $x$ out of $- x \cdot 4$ .

$\frac{x (3 \cdot 3) + x (- 1 \cdot 4)}{12} - 5 = 0$

Step 1.10.1.1.3

Factor $x$ out of $x (3 \cdot 3) + x (- 1 \cdot 4)$ .

$\frac{x (3 \cdot 3 - 1 \cdot 4)}{12} - 5 = 0$

Step 1.10.1.2

Multiply $3$ by $3$ .

$\frac{x (9 - 1 \cdot 4)}{12} - 5 = 0$

Step 1.10.1.3

Multiply $- 1$ by $4$ .

$\frac{x (9 - 4)}{12} - 5 = 0$

Step 1.10.1.4

Subtract $4$ from $9$ .

$\frac{x \cdot 5}{12} - 5 = 0$

Step 1.10.2

Move $5$ to the left of $x$ .

$\frac{5 x}{12} - 5 = 0$

Step 2

Add $5$ to both sides of the equation.

$\frac{5 x}{12} = 5$

Step 3

Multiply both sides of the equation by $\frac{12}{5}$ .

$\frac{12}{5} \cdot \frac{5 x}{12} = \frac{12}{5} \cdot 5$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{12}{5} \cdot \frac{5 x}{12}$ .

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Step 4.1.1.1

Cancel the common factor of $12$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{12}{5} \cdot \frac{5 x}{12} = \frac{12}{5} \cdot 5$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{12}{5} \cdot 5$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{12}{5} \cdot 5$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{12}{5} \cdot 5$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{12}{5} \cdot 5$

Step 4.2

Simplify the right 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.

$x = \frac{12}{5} \cdot 5$

Step 4.2.1.2

Rewrite the expression.

$x = 12$