Algebra Examples

$\frac{2}{7 x} + \frac{1}{4} = \frac{53}{14 x} - \frac{1}{3}$

Move all the expressions to the left side of the equation.

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Subtract $\frac{53}{14 x}$ from both sides of the equation.

$\frac{2}{7 x} + \frac{1}{4} - \frac{53}{14 x} = - \frac{1}{3}$

Add $\frac{1}{3}$ to both sides of the equation.

$\frac{2}{7 x} + \frac{1}{4} - \frac{53}{14 x} + \frac{1}{3} = 0$

Simplify $\frac{2}{7 x} + \frac{1}{4} - \frac{53}{14 x} + \frac{1}{3}$ .

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

$\frac{2}{7 x} \cdot \frac{2}{2} - \frac{53}{14 x} + \frac{1}{4} + \frac{1}{3} = 0$

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

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

$\frac{2 \cdot 2}{7 x \cdot 2} - \frac{53}{14 x} + \frac{1}{4} + \frac{1}{3} = 0$

Multiply $2$ by $7$ .

$\frac{2 \cdot 2}{14 x} - \frac{53}{14 x} + \frac{1}{4} + \frac{1}{3} = 0$

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 - 53}{14 x} + \frac{1}{4} + \frac{1}{3} = 0$

Simplify the numerator.

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Multiply $2$ by $2$ .

$\frac{4 - 53}{14 x} + \frac{1}{4} + \frac{1}{3} = 0$

Subtract $53$ from $4$ .

$\frac{- 49}{14 x} + \frac{1}{4} + \frac{1}{3} = 0$

Simplify each term.

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Cancel the common factor of $- 49$ and $14$ .

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Factor $7$ out of $- 49$ .

$\frac{7 (- 7)}{14 x} + \frac{1}{4} + \frac{1}{3} = 0$

Cancel the common factors.

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Factor $7$ out of $14 x$ .

$\frac{7 (- 7)}{7 (2 x)} + \frac{1}{4} + \frac{1}{3} = 0$

Cancel the common factor.

$\frac{7 \cdot - 7}{7 (2 x)} + \frac{1}{4} + \frac{1}{3} = 0$

Rewrite the expression.

$\frac{- 7}{2 x} + \frac{1}{4} + \frac{1}{3} = 0$

Move the negative in front of the fraction.

$- \frac{7}{2 x} + \frac{1}{4} + \frac{1}{3} = 0$

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{7}{2 x} + \frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3} = 0$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{7}{2 x} + \frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{4}{4} = 0$

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

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Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$- \frac{7}{2 x} + \frac{3}{4 \cdot 3} + \frac{1}{3} \cdot \frac{4}{4} = 0$

Multiply $4$ by $3$ .

$- \frac{7}{2 x} + \frac{3}{12} + \frac{1}{3} \cdot \frac{4}{4} = 0$

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$- \frac{7}{2 x} + \frac{3}{12} + \frac{4}{3 \cdot 4} = 0$

Multiply $3$ by $4$ .

$- \frac{7}{2 x} + \frac{3}{12} + \frac{4}{12} = 0$

Combine the numerators over the common denominator.

$- \frac{7}{2 x} + \frac{3 + 4}{12} = 0$

Add $3$ and $4$ .

$- \frac{7}{2 x} + \frac{7}{12} = 0$

Set the denominator in $\frac{7}{2 x}$ equal to $0$ to find where the expression is undefined.

$2 x = 0$

Divide each term in $2 x = 0$ by $2$ and simplify.

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Divide each term in $2 x = 0$ by $2$ .

$\frac{2 x}{2} = \frac{0}{2}$

Simplify the left side.

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Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 x}{2} = \frac{0}{2}$

Divide $x$ by $1$ .

$x = \frac{0}{2}$

Simplify the right side.

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Divide $0$ by $2$ .

$x = 0$