Algebra Examples

$\frac{7}{12} x - \frac{4}{5} x - \frac{1}{3} x = - \frac{1}{4}$

Step 1

Simplify $\frac{7}{12} x - \frac{4}{5} x - \frac{1}{3} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{7}{12}$ and $x$ .

$\frac{7 x}{12} - \frac{4}{5} x - \frac{1}{3} x = - \frac{1}{4}$

Step 1.1.2

Combine $x$ and $\frac{4}{5}$ .

$\frac{7 x}{12} - \frac{x \cdot 4}{5} - \frac{1}{3} x = - \frac{1}{4}$

Step 1.1.3

Move $4$ to the left of $x$ .

$\frac{7 x}{12} - \frac{4 \cdot x}{5} - \frac{1}{3} x = - \frac{1}{4}$

Step 1.1.4

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

$\frac{7 x}{12} - \frac{4 x}{5} - \frac{x}{3} = - \frac{1}{4}$

Step 1.2

Find the common denominator.

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Step 1.2.1

Multiply $\frac{7 x}{12}$ by $\frac{5}{5}$ .

$\frac{7 x}{12} \cdot \frac{5}{5} - \frac{4 x}{5} - \frac{x}{3} = - \frac{1}{4}$

Step 1.2.2

Multiply $\frac{7 x}{12}$ by $\frac{5}{5}$ .

$\frac{7 x \cdot 5}{12 \cdot 5} - \frac{4 x}{5} - \frac{x}{3} = - \frac{1}{4}$

Step 1.2.3

Multiply $\frac{4 x}{5}$ by $\frac{12}{12}$ .

$\frac{7 x \cdot 5}{12 \cdot 5} - (\frac{4 x}{5} \cdot \frac{12}{12}) - \frac{x}{3} = - \frac{1}{4}$

Step 1.2.4

Multiply $\frac{4 x}{5}$ by $\frac{12}{12}$ .

$\frac{7 x \cdot 5}{12 \cdot 5} - \frac{4 x \cdot 12}{5 \cdot 12} - \frac{x}{3} = - \frac{1}{4}$

Step 1.2.5

Multiply $\frac{x}{3}$ by $\frac{20}{20}$ .

$\frac{7 x \cdot 5}{12 \cdot 5} - \frac{4 x \cdot 12}{5 \cdot 12} - (\frac{x}{3} \cdot \frac{20}{20}) = - \frac{1}{4}$

Step 1.2.6

Multiply $\frac{x}{3}$ by $\frac{20}{20}$ .

$\frac{7 x \cdot 5}{12 \cdot 5} - \frac{4 x \cdot 12}{5 \cdot 12} - \frac{x \cdot 20}{3 \cdot 20} = - \frac{1}{4}$

Step 1.2.7

Reorder the factors of $12 \cdot 5$ .

$\frac{7 x \cdot 5}{5 \cdot 12} - \frac{4 x \cdot 12}{5 \cdot 12} - \frac{x \cdot 20}{3 \cdot 20} = - \frac{1}{4}$

Step 1.2.8

Multiply $5$ by $12$ .

$\frac{7 x \cdot 5}{60} - \frac{4 x \cdot 12}{5 \cdot 12} - \frac{x \cdot 20}{3 \cdot 20} = - \frac{1}{4}$

Step 1.2.9

Multiply $5$ by $12$ .

$\frac{7 x \cdot 5}{60} - \frac{4 x \cdot 12}{60} - \frac{x \cdot 20}{3 \cdot 20} = - \frac{1}{4}$

Step 1.2.10

Multiply $3$ by $20$ .

$\frac{7 x \cdot 5}{60} - \frac{4 x \cdot 12}{60} - \frac{x \cdot 20}{60} = - \frac{1}{4}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{7 x \cdot 5 - 4 x \cdot 12 - x \cdot 20}{60} = - \frac{1}{4}$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $5$ by $7$ .

$\frac{35 x - 4 x \cdot 12 - x \cdot 20}{60} = - \frac{1}{4}$

Step 1.4.2

Multiply $12$ by $- 4$ .

$\frac{35 x - 48 x - x \cdot 20}{60} = - \frac{1}{4}$

Step 1.4.3

Multiply $20$ by $- 1$ .

$\frac{35 x - 48 x - 20 x}{60} = - \frac{1}{4}$

Step 1.5

Simplify terms.

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Step 1.5.1

Subtract $48 x$ from $35 x$ .

$\frac{- 13 x - 20 x}{60} = - \frac{1}{4}$

Step 1.5.2

Subtract $20 x$ from $- 13 x$ .

$\frac{- 33 x}{60} = - \frac{1}{4}$

Step 1.5.3

Cancel the common factor of $- 33$ and $60$ .

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Step 1.5.3.1

Factor $3$ out of $- 33 x$ .

$\frac{3 (- 11 x)}{60} = - \frac{1}{4}$

Step 1.5.3.2

Cancel the common factors.

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Step 1.5.3.2.1

Factor $3$ out of $60$ .

$\frac{3 (- 11 x)}{3 (20)} = - \frac{1}{4}$

Step 1.5.3.2.2

Cancel the common factor.

$\frac{3 (- 11 x)}{3 \cdot 20} = - \frac{1}{4}$

Step 1.5.3.2.3

Rewrite the expression.

$\frac{- 11 x}{20} = - \frac{1}{4}$

Step 1.5.4

Move the negative in front of the fraction.

$- \frac{11 x}{20} = - \frac{1}{4}$

Step 2

Multiply both sides of the equation by $- \frac{20}{11}$ .

$- \frac{20}{11} (- \frac{11 x}{20}) = - \frac{20}{11} (- \frac{1}{4})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- \frac{20}{11} (- \frac{11 x}{20})$ .

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Step 3.1.1.1

Cancel the common factor of $20$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{20}{11}$ into the numerator.

$\frac{- 20}{11} (- \frac{11 x}{20}) = - \frac{20}{11} (- \frac{1}{4})$

Step 3.1.1.1.2

Move the leading negative in $- \frac{11 x}{20}$ into the numerator.

$\frac{- 20}{11} \cdot \frac{- 11 x}{20} = - \frac{20}{11} (- \frac{1}{4})$

Step 3.1.1.1.3

Factor $20$ out of $- 20$ .

$\frac{20 (- 1)}{11} \cdot \frac{- 11 x}{20} = - \frac{20}{11} (- \frac{1}{4})$

Step 3.1.1.1.4

Cancel the common factor.

$\frac{20 \cdot - 1}{11} \cdot \frac{- 11 x}{20} = - \frac{20}{11} (- \frac{1}{4})$

Step 3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{11} (- 11 x) = - \frac{20}{11} (- \frac{1}{4})$

Step 3.1.1.2

Cancel the common factor of $11$ .

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Step 3.1.1.2.1

Factor $11$ out of $- 11 x$ .

$\frac{- 1}{11} (11 (- x)) = - \frac{20}{11} (- \frac{1}{4})$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{11} (11 (- x)) = - \frac{20}{11} (- \frac{1}{4})$

Step 3.1.1.2.3

Rewrite the expression.

$- - x = - \frac{20}{11} (- \frac{1}{4})$

Step 3.1.1.3

Multiply.

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Step 3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{20}{11} (- \frac{1}{4})$

Step 3.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{20}{11} (- \frac{1}{4})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{20}{11} (- \frac{1}{4})$ .

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Step 3.2.1.1

Cancel the common factor of $4$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{20}{11}$ into the numerator.

$x = \frac{- 20}{11} (- \frac{1}{4})$

Step 3.2.1.1.2

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$x = \frac{- 20}{11} \cdot \frac{- 1}{4}$

Step 3.2.1.1.3

Factor $4$ out of $- 20$ .

$x = \frac{4 (- 5)}{11} \cdot \frac{- 1}{4}$

Step 3.2.1.1.4

Cancel the common factor.

$x = \frac{4 \cdot - 5}{11} \cdot \frac{- 1}{4}$

Step 3.2.1.1.5

Rewrite the expression.

$x = \frac{- 5}{11} \cdot - 1$

Step 3.2.1.2

Combine $\frac{- 5}{11}$ and $- 1$ .

$x = \frac{- 5 \cdot - 1}{11}$

Step 3.2.1.3

Multiply $- 5$ by $- 1$ .

$x = \frac{5}{11}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{11}$

Decimal Form:

$x = 0.\overline{45}$