Algebra Examples

$\frac{4}{5} x - \frac{1}{4} = \frac{7}{10} x - \frac{4}{5}$

Step 1

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

$\frac{4 x}{5} - \frac{1}{4} = \frac{7}{10} x - \frac{4}{5}$

Step 2

Combine $\frac{7}{10}$ and $x$ .

$\frac{4 x}{5} - \frac{1}{4} = \frac{7 x}{10} - \frac{4}{5}$

Step 3

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

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Step 3.1

Subtract $\frac{7 x}{10}$ from both sides of the equation.

$\frac{4 x}{5} - \frac{1}{4} - \frac{7 x}{10} = - \frac{4}{5}$

Step 3.2

To write $\frac{4 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 x}{5} \cdot \frac{2}{2} - \frac{7 x}{10} - \frac{1}{4} = - \frac{4}{5}$

Step 3.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{4 x}{5}$ by $\frac{2}{2}$ .

$\frac{4 x \cdot 2}{5 \cdot 2} - \frac{7 x}{10} - \frac{1}{4} = - \frac{4}{5}$

Step 3.3.2

Multiply $5$ by $2$ .

$\frac{4 x \cdot 2}{10} - \frac{7 x}{10} - \frac{1}{4} = - \frac{4}{5}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{4 x \cdot 2 - 7 x}{10} - \frac{1}{4} = - \frac{4}{5}$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $x$ out of $4 x \cdot 2 - 7 x$ .

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Step 3.5.1.1.1

Factor $x$ out of $4 x \cdot 2$ .

$\frac{x (4 \cdot 2) - 7 x}{10} - \frac{1}{4} = - \frac{4}{5}$

Step 3.5.1.1.2

Factor $x$ out of $- 7 x$ .

$\frac{x (4 \cdot 2) + x \cdot - 7}{10} - \frac{1}{4} = - \frac{4}{5}$

Step 3.5.1.1.3

Factor $x$ out of $x (4 \cdot 2) + x \cdot - 7$ .

$\frac{x (4 \cdot 2 - 7)}{10} - \frac{1}{4} = - \frac{4}{5}$

Step 3.5.1.2

Multiply $4$ by $2$ .

$\frac{x (8 - 7)}{10} - \frac{1}{4} = - \frac{4}{5}$

Step 3.5.1.3

Subtract $7$ from $8$ .

$\frac{x \cdot 1}{10} - \frac{1}{4} = - \frac{4}{5}$

Step 3.5.2

Multiply $x$ by $1$ .

$\frac{x}{10} - \frac{1}{4} = - \frac{4}{5}$

Step 4

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

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Step 4.1

Add $\frac{1}{4}$ to both sides of the equation.

$\frac{x}{10} = - \frac{4}{5} + \frac{1}{4}$

Step 4.2

To write $- \frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{10} = - \frac{4}{5} \cdot \frac{4}{4} + \frac{1}{4}$

Step 4.3

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{10} = - \frac{4}{5} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{5}{5}$

Step 4.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.1

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

$\frac{x}{10} = - \frac{4 \cdot 4}{5 \cdot 4} + \frac{1}{4} \cdot \frac{5}{5}$

Step 4.4.2

Multiply $5$ by $4$ .

$\frac{x}{10} = - \frac{4 \cdot 4}{20} + \frac{1}{4} \cdot \frac{5}{5}$

Step 4.4.3

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$\frac{x}{10} = - \frac{4 \cdot 4}{20} + \frac{5}{4 \cdot 5}$

Step 4.4.4

Multiply $4$ by $5$ .

$\frac{x}{10} = - \frac{4 \cdot 4}{20} + \frac{5}{20}$

Step 4.5

Combine the numerators over the common denominator.

$\frac{x}{10} = \frac{- 4 \cdot 4 + 5}{20}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Multiply $- 4$ by $4$ .

$\frac{x}{10} = \frac{- 16 + 5}{20}$

Step 4.6.2

Add $- 16$ and $5$ .

$\frac{x}{10} = \frac{- 11}{20}$

Step 4.7

Move the negative in front of the fraction.

$\frac{x}{10} = - \frac{11}{20}$

Step 5

Multiply both sides of the equation by $10$ .

$10 \frac{x}{10} = 10 (- \frac{11}{20})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $10$ .

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Step 6.1.1.1

Cancel the common factor.

$10 \frac{x}{10} = 10 (- \frac{11}{20})$

Step 6.1.1.2

Rewrite the expression.

$x = 10 (- \frac{11}{20})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $10 (- \frac{11}{20})$ .

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Step 6.2.1.1

Cancel the common factor of $10$ .

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Step 6.2.1.1.1

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

$x = 10 (\frac{- 11}{20})$

Step 6.2.1.1.2

Factor $10$ out of $20$ .

$x = 10 \frac{- 11}{10 (2)}$

Step 6.2.1.1.3

Cancel the common factor.

$x = 10 \frac{- 11}{10 \cdot 2}$

Step 6.2.1.1.4

Rewrite the expression.

$x = \frac{- 11}{2}$

Step 6.2.1.2

Move the negative in front of the fraction.

$x = - \frac{11}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{11}{2}$

Decimal Form:

$x = - 5.5$

Mixed Number Form:

$x = - 5 \frac{1}{2}$