Algebra Examples

$\frac{1}{5} (3 x - 0.5) + \frac{1}{6} = \frac{x}{5} + 0.5$

Step 1

Simplify $\frac{1}{5} \cdot (3 x - 0.5) + \frac{1}{6}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{1}{5} (3 x) + \frac{1}{5} \cdot - 0.5 + \frac{1}{6} = \frac{x}{5} + 0.5$

Step 1.1.2

Multiply $\frac{1}{5} (3 x)$ .

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Step 1.1.2.1

Combine $3$ and $\frac{1}{5}$ .

$\frac{3}{5} x + \frac{1}{5} \cdot - 0.5 + \frac{1}{6} = \frac{x}{5} + 0.5$

Step 1.1.2.2

Combine $\frac{3}{5}$ and $x$ .

$\frac{3 x}{5} + \frac{1}{5} \cdot - 0.5 + \frac{1}{6} = \frac{x}{5} + 0.5$

Step 1.1.3

Cancel the common factor of $0.5$ .

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Step 1.1.3.1

Factor $0.5$ out of $5$ .

$\frac{3 x}{5} + \frac{1}{0.5 (10)} \cdot - 0.5 + \frac{1}{6} = \frac{x}{5} + 0.5$

Step 1.1.3.2

Factor $0.5$ out of $- 0.5$ .

$\frac{3 x}{5} + \frac{1}{0.5 \cdot 10} \cdot (0.5 \cdot - 1) + \frac{1}{6} = \frac{x}{5} + 0.5$

Step 1.1.3.3

Cancel the common factor.

$\frac{3 x}{5} + \frac{1}{0.5 \cdot 10} \cdot (0.5 \cdot - 1) + \frac{1}{6} = \frac{x}{5} + 0.5$

Step 1.1.3.4

Rewrite the expression.

$\frac{3 x}{5} + \frac{1}{10} \cdot - 1 + \frac{1}{6} = \frac{x}{5} + 0.5$

Step 1.1.4

Combine $\frac{1}{10}$ and $- 1$ .

$\frac{3 x}{5} + \frac{- 1}{10} + \frac{1}{6} = \frac{x}{5} + 0.5$

Step 1.1.5

Move the negative in front of the fraction.

$\frac{3 x}{5} - \frac{1}{10} + \frac{1}{6} = \frac{x}{5} + 0.5$

Step 1.2

To write $- \frac{1}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 x}{5} - \frac{1}{10} \cdot \frac{3}{3} + \frac{1}{6} = \frac{x}{5} + 0.5$

Step 1.3

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 x}{5} - \frac{1}{10} \cdot \frac{3}{3} + \frac{1}{6} \cdot \frac{5}{5} = \frac{x}{5} + 0.5$

Step 1.4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{1}{10}$ by $\frac{3}{3}$ .

$\frac{3 x}{5} - \frac{3}{10 \cdot 3} + \frac{1}{6} \cdot \frac{5}{5} = \frac{x}{5} + 0.5$

Step 1.4.2

Multiply $10$ by $3$ .

$\frac{3 x}{5} - \frac{3}{30} + \frac{1}{6} \cdot \frac{5}{5} = \frac{x}{5} + 0.5$

Step 1.4.3

Multiply $\frac{1}{6}$ by $\frac{5}{5}$ .

$\frac{3 x}{5} - \frac{3}{30} + \frac{5}{6 \cdot 5} = \frac{x}{5} + 0.5$

Step 1.4.4

Multiply $6$ by $5$ .

$\frac{3 x}{5} - \frac{3}{30} + \frac{5}{30} = \frac{x}{5} + 0.5$

Step 1.5

Simplify the expression.

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Step 1.5.1

Combine the numerators over the common denominator.

$\frac{3 x}{5} + \frac{- 3 + 5}{30} = \frac{x}{5} + 0.5$

Step 1.5.2

Add $- 3$ and $5$ .

$\frac{3 x}{5} + \frac{2}{30} = \frac{x}{5} + 0.5$

Step 1.6

Cancel the common factor of $2$ and $30$ .

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Step 1.6.1

Factor $2$ out of $2$ .

$\frac{3 x}{5} + \frac{2 (1)}{30} = \frac{x}{5} + 0.5$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $2$ out of $30$ .

$\frac{3 x}{5} + \frac{2 \cdot 1}{2 \cdot 15} = \frac{x}{5} + 0.5$

Step 1.6.2.2

Cancel the common factor.

$\frac{3 x}{5} + \frac{2 \cdot 1}{2 \cdot 15} = \frac{x}{5} + 0.5$

Step 1.6.2.3

Rewrite the expression.

$\frac{3 x}{5} + \frac{1}{15} = \frac{x}{5} + 0.5$

Step 2

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

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Step 2.1

Subtract $\frac{x}{5}$ from both sides of the equation.

$\frac{3 x}{5} + \frac{1}{15} - \frac{x}{5} = 0.5$

Step 2.2

Combine the numerators over the common denominator.

$\frac{3 x - x}{5} + \frac{1}{15} = 0.5$

Step 2.3

Subtract $x$ from $3 x$ .

$\frac{2 x}{5} + \frac{1}{15} = 0.5$

Step 3

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

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Step 3.1

Subtract $\frac{1}{15}$ from both sides of the equation.

$\frac{2 x}{5} = 0.5 - \frac{1}{15}$

Step 3.2

To write $0.5$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{2 x}{5} = 0.5 \cdot \frac{15}{15} - \frac{1}{15}$

Step 3.3

Combine $0.5$ and $\frac{15}{15}$ .

$\frac{2 x}{5} = \frac{0.5 \cdot 15}{15} - \frac{1}{15}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{2 x}{5} = \frac{0.5 \cdot 15 - 1}{15}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $0.5$ by $15$ .

$\frac{2 x}{5} = \frac{7.5 - 1}{15}$

Step 3.5.2

Subtract $1$ from $7.5$ .

$\frac{2 x}{5} = \frac{6.5}{15}$

Step 3.6

Divide $6.5$ by $15$ .

$\frac{2 x}{5} = 0.4\overline{3}$

Step 4

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} \cdot \frac{2 x}{5} = \frac{5}{2} \cdot 0.4\overline{3}$

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 $\frac{5}{2} \cdot \frac{2 x}{5}$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 x}{5} = \frac{5}{2} \cdot 0.4\overline{3}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{5}{2} \cdot 0.4\overline{3}$

Step 5.1.1.2

Cancel the common factor of $2$ .

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Step 5.1.1.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{5}{2} \cdot 0.4\overline{3}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{5}{2} \cdot 0.4\overline{3}$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{5}{2} \cdot 0.4\overline{3}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{5}{2} \cdot 0.4\overline{3}$ .

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Step 5.2.1.1

Multiply $\frac{5}{2} \cdot 0.4\overline{3}$ .

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Step 5.2.1.1.1

Combine $\frac{5}{2}$ and $0.4\overline{3}$ .

$x = \frac{5 \cdot 0.4\overline{3}}{2}$

Step 5.2.1.1.2

Multiply $5$ by $0.4\overline{3}$ .

$x = \frac{2.1\overline{6}}{2}$

Step 5.2.1.2

Divide $2.1\overline{6}$ by $2$ .

$x = 1.08\overline{3}$