Precalculus Examples

$\frac{1}{7} x - \frac{3}{4} = 1 - \frac{x}{2}$

Step 1

Combine $\frac{1}{7}$ and $x$ .

$\frac{x}{7} - \frac{3}{4} = 1 - \frac{x}{2}$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Add $\frac{x}{2}$ to both sides of the equation.

$\frac{x}{7} - \frac{3}{4} + \frac{x}{2} = 1$

Step 2.2

To write $\frac{x}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{7} \cdot \frac{2}{2} + \frac{x}{2} - \frac{3}{4} = 1$

Step 2.3

To write $\frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{x}{7} \cdot \frac{2}{2} + \frac{x}{2} \cdot \frac{7}{7} - \frac{3}{4} = 1$

Step 2.4

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{x}{7}$ by $\frac{2}{2}$ .

$\frac{x \cdot 2}{7 \cdot 2} + \frac{x}{2} \cdot \frac{7}{7} - \frac{3}{4} = 1$

Step 2.4.2

Multiply $7$ by $2$ .

$\frac{x \cdot 2}{14} + \frac{x}{2} \cdot \frac{7}{7} - \frac{3}{4} = 1$

Step 2.4.3

Multiply $\frac{x}{2}$ by $\frac{7}{7}$ .

$\frac{x \cdot 2}{14} + \frac{x \cdot 7}{2 \cdot 7} - \frac{3}{4} = 1$

Step 2.4.4

Multiply $2$ by $7$ .

$\frac{x \cdot 2}{14} + \frac{x \cdot 7}{14} - \frac{3}{4} = 1$

Step 2.5

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + x \cdot 7}{14} - \frac{3}{4} = 1$

Step 2.6

Reorder $x$ and $7$ .

$\frac{2 \cdot x + 7 \cdot x}{14} - \frac{3}{4} = 1$

Step 2.7

Add $2 \cdot x$ and $7 \cdot x$ .

$\frac{9 x}{14} - \frac{3}{4} = 1$

Step 3

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

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Step 3.1

Add $\frac{3}{4}$ to both sides of the equation.

$\frac{9 x}{14} = 1 + \frac{3}{4}$

Step 3.2

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

$\frac{9 x}{14} = \frac{4}{4} + \frac{3}{4}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{9 x}{14} = \frac{4 + 3}{4}$

Step 3.4

Add $4$ and $3$ .

$\frac{9 x}{14} = \frac{7}{4}$

Step 4

Multiply both sides of the equation by $\frac{14}{9}$ .

$\frac{14}{9} \cdot \frac{9 x}{14} = \frac{14}{9} \cdot \frac{7}{4}$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{14}{9} \cdot \frac{9 x}{14}$ .

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Step 5.1.1.1

Cancel the common factor of $14$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{14}{9} \cdot \frac{9 x}{14} = \frac{14}{9} \cdot \frac{7}{4}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 x) = \frac{14}{9} \cdot \frac{7}{4}$

Step 5.1.1.2

Cancel the common factor of $9$ .

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Step 5.1.1.2.1

Factor $9$ out of $9 x$ .

$\frac{1}{9} (9 (x)) = \frac{14}{9} \cdot \frac{7}{4}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 x) = \frac{14}{9} \cdot \frac{7}{4}$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{14}{9} \cdot \frac{7}{4}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{14}{9} \cdot \frac{7}{4}$ .

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Factor $2$ out of $14$ .

$x = \frac{2 (7)}{9} \cdot \frac{7}{4}$

Step 5.2.1.1.2

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 7}{9} \cdot \frac{7}{2 \cdot 2}$

Step 5.2.1.1.3

Cancel the common factor.

$x = \frac{2 \cdot 7}{9} \cdot \frac{7}{2 \cdot 2}$

Step 5.2.1.1.4

Rewrite the expression.

$x = \frac{7}{9} \cdot \frac{7}{2}$

Step 5.2.1.2

Multiply $\frac{7}{9}$ by $\frac{7}{2}$ .

$x = \frac{7 \cdot 7}{9 \cdot 2}$

Step 5.2.1.3

Multiply.

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Step 5.2.1.3.1

Multiply $7$ by $7$ .

$x = \frac{49}{9 \cdot 2}$

Step 5.2.1.3.2

Multiply $9$ by $2$ .

$x = \frac{49}{18}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{49}{18}$

Decimal Form:

$x = 2.7\overline{2}$

Mixed Number Form:

$x = 2 \frac{13}{18}$