Algebra Examples

$\frac{7}{2 x} - \frac{5}{3 x} = \frac{22}{3}$

Step 1

Subtract $\frac{22}{3}$ from both sides of the equation.

$\frac{7}{2 x} - \frac{5}{3 x} - \frac{22}{3} = 0$

Step 2

Simplify $\frac{7}{2 x} - \frac{5}{3 x} - \frac{22}{3}$ .

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Step 2.1

To write $\frac{7}{2 x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7}{2 x} \cdot \frac{3}{3} - \frac{5}{3 x} - \frac{22}{3} = 0$

Step 2.2

To write $- \frac{5}{3 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7}{2 x} \cdot \frac{3}{3} - \frac{5}{3 x} \cdot \frac{2}{2} - \frac{22}{3} = 0$

Step 2.3

Write each expression with a common denominator of $6 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{7}{2 x}$ by $\frac{3}{3}$ .

$\frac{7 \cdot 3}{2 x \cdot 3} - \frac{5}{3 x} \cdot \frac{2}{2} - \frac{22}{3} = 0$

Step 2.3.2

Multiply $3$ by $2$ .

$\frac{7 \cdot 3}{6 x} - \frac{5}{3 x} \cdot \frac{2}{2} - \frac{22}{3} = 0$

Step 2.3.3

Multiply $\frac{5}{3 x}$ by $\frac{2}{2}$ .

$\frac{7 \cdot 3}{6 x} - \frac{5 \cdot 2}{3 x \cdot 2} - \frac{22}{3} = 0$

Step 2.3.4

Multiply $2$ by $3$ .

$\frac{7 \cdot 3}{6 x} - \frac{5 \cdot 2}{6 x} - \frac{22}{3} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 \cdot 3 - 5 \cdot 2}{6 x} - \frac{22}{3} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $7$ by $3$ .

$\frac{21 - 5 \cdot 2}{6 x} - \frac{22}{3} = 0$

Step 2.5.2

Multiply $- 5$ by $2$ .

$\frac{21 - 10}{6 x} - \frac{22}{3} = 0$

Step 2.5.3

Subtract $10$ from $21$ .

$\frac{11}{6 x} - \frac{22}{3} = 0$

Step 3

To write $- \frac{22}{3}$ as a fraction with a common denominator, multiply by $\frac{2 x}{2 x}$ .

$\frac{11}{6 x} - \frac{22}{3} \cdot \frac{2 x}{2 x} = 0$

Step 4

Write each expression with a common denominator of $6 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{22}{3}$ by $\frac{2 x}{2 x}$ .

$\frac{11}{6 x} - \frac{22 (2 x)}{3 (2 x)} = 0$

Step 4.2

Multiply $2$ by $3$ .

$\frac{11}{6 x} - \frac{22 (2 x)}{6 x} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{11 - 22 (2 x)}{6 x} = 0$

Step 6

Remove parentheses.

$\frac{11 - 22 \cdot (2 x)}{6 x} = 0$

Step 7

Simplify the numerator.

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Step 7.1

Factor $11$ out of $11 - 22 \cdot 2 x$ .

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Step 7.1.1

Factor $11$ out of $11$ .

$\frac{11 (1) - 22 \cdot (2 x)}{6 x} = 0$

Step 7.1.2

Factor $11$ out of $- 22 \cdot 2 x$ .

$\frac{11 (1) + 11 (- 2 \cdot (2 x))}{6 x} = 0$

Step 7.1.3

Factor $11$ out of $11 (1) + 11 (- 2 \cdot 2 x)$ .

$\frac{11 (1 - 2 \cdot (2 x))}{6 x} = 0$

Step 7.2

Multiply $- 2$ by $2$ .

$\frac{11 (1 - 4 x)}{6 x} = 0$

Step 8

Set the numerator equal to zero.

$11 (1 - 4 x) = 0$

Step 9

Solve the equation for $x$ .

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Step 9.1

Divide each term in $11 (1 - 4 x) = 0$ by $11$ and simplify.

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Step 9.1.1

Divide each term in $11 (1 - 4 x) = 0$ by $11$ .

$\frac{11 (1 - 4 x)}{11} = \frac{0}{11}$

Step 9.1.2

Simplify the left side.

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Step 9.1.2.1

Cancel the common factor of $11$ .

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Step 9.1.2.1.1

Cancel the common factor.

$\frac{11 (1 - 4 x)}{11} = \frac{0}{11}$

Step 9.1.2.1.2

Divide $1 - 4 x$ by $1$ .

$1 - 4 x = \frac{0}{11}$

Step 9.1.3

Simplify the right side.

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Step 9.1.3.1

Divide $0$ by $11$ .

$1 - 4 x = 0$

Step 9.2

Subtract $1$ from both sides of the equation.

$- 4 x = - 1$

Step 9.3

Divide each term in $- 4 x = - 1$ by $- 4$ and simplify.

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Step 9.3.1

Divide each term in $- 4 x = - 1$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 1}{- 4}$

Step 9.3.2

Simplify the left side.

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Step 9.3.2.1

Cancel the common factor of $- 4$ .

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Step 9.3.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 1}{- 4}$

Step 9.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{- 4}$

Step 9.3.3

Simplify the right side.

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Step 9.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{1}{4}$