Algebra Examples

$- \frac{1}{2} x - \frac{3}{5} = \frac{1}{5} x$

Step 1

Combine $x$ and $\frac{1}{2}$ .

$- \frac{x}{2} - \frac{3}{5} = \frac{1}{5} x$

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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Step 3.4.1

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

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

Step 3.4.2

Multiply $2$ by $5$ .

$- \frac{x \cdot 5}{10} - \frac{x}{5} \cdot \frac{2}{2} - \frac{3}{5} = 0$

Step 3.4.3

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

$- \frac{x \cdot 5}{10} - \frac{x \cdot 2}{5 \cdot 2} - \frac{3}{5} = 0$

Step 3.4.4

Multiply $5$ by $2$ .

$- \frac{x \cdot 5}{10} - \frac{x \cdot 2}{10} - \frac{3}{5} = 0$

Step 3.5

Combine the numerators over the common denominator.

$\frac{- x \cdot 5 - x \cdot 2}{10} - \frac{3}{5} = 0$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Factor $x$ out of $- x \cdot 5 - x \cdot 2$ .

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Step 3.6.1.1.1

Factor $x$ out of $- x \cdot 5$ .

$\frac{x (- 1 \cdot 5) - x \cdot 2}{10} - \frac{3}{5} = 0$

Step 3.6.1.1.2

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

$\frac{x (- 1 \cdot 5) + x (- 1 \cdot 2)}{10} - \frac{3}{5} = 0$

Step 3.6.1.1.3

Factor $x$ out of $x (- 1 \cdot 5) + x (- 1 \cdot 2)$ .

$\frac{x (- 1 \cdot 5 - 1 \cdot 2)}{10} - \frac{3}{5} = 0$

Step 3.6.1.2

Multiply $- 1$ by $5$ .

$\frac{x (- 5 - 1 \cdot 2)}{10} - \frac{3}{5} = 0$

Step 3.6.1.3

Multiply $- 1$ by $2$ .

$\frac{x (- 5 - 2)}{10} - \frac{3}{5} = 0$

Step 3.6.1.4

Subtract $2$ from $- 5$ .

$\frac{x \cdot - 7}{10} - \frac{3}{5} = 0$

Step 3.6.2

Move $- 7$ to the left of $x$ .

$\frac{- 7 \cdot x}{10} - \frac{3}{5} = 0$

Step 3.6.3

Move the negative in front of the fraction.

$- \frac{7 x}{10} - \frac{3}{5} = 0$

Step 4

Add $\frac{3}{5}$ to both sides of the equation.

$- \frac{7 x}{10} = \frac{3}{5}$

Step 5

Multiply both sides of the equation by $- \frac{10}{7}$ .

$- \frac{10}{7} (- \frac{7 x}{10}) = - \frac{10}{7} \cdot \frac{3}{5}$

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

Simplify $- \frac{10}{7} (- \frac{7 x}{10})$ .

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Step 6.1.1.1

Cancel the common factor of $10$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{10}{7}$ into the numerator.

$\frac{- 10}{7} (- \frac{7 x}{10}) = - \frac{10}{7} \cdot \frac{3}{5}$

Step 6.1.1.1.2

Move the leading negative in $- \frac{7 x}{10}$ into the numerator.

$\frac{- 10}{7} \cdot \frac{- 7 x}{10} = - \frac{10}{7} \cdot \frac{3}{5}$

Step 6.1.1.1.3

Factor $10$ out of $- 10$ .

$\frac{10 (- 1)}{7} \cdot \frac{- 7 x}{10} = - \frac{10}{7} \cdot \frac{3}{5}$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{10 \cdot - 1}{7} \cdot \frac{- 7 x}{10} = - \frac{10}{7} \cdot \frac{3}{5}$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{7} (- 7 x) = - \frac{10}{7} \cdot \frac{3}{5}$

Step 6.1.1.2

Cancel the common factor of $7$ .

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Step 6.1.1.2.1

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

$\frac{- 1}{7} (7 (- x)) = - \frac{10}{7} \cdot \frac{3}{5}$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{7} (7 (- x)) = - \frac{10}{7} \cdot \frac{3}{5}$

Step 6.1.1.2.3

Rewrite the expression.

$- - x = - \frac{10}{7} \cdot \frac{3}{5}$

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{10}{7} \cdot \frac{3}{5}$

Step 6.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{10}{7} \cdot \frac{3}{5}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{10}{7} \cdot \frac{3}{5}$ .

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Step 6.2.1.1

Cancel the common factor of $5$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{10}{7}$ into the numerator.

$x = \frac{- 10}{7} \cdot \frac{3}{5}$

Step 6.2.1.1.2

Factor $5$ out of $- 10$ .

$x = \frac{5 (- 2)}{7} \cdot \frac{3}{5}$

Step 6.2.1.1.3

Cancel the common factor.

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

Step 6.2.1.1.4

Rewrite the expression.

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

Step 6.2.1.2

Combine $\frac{- 2}{7}$ and $3$ .

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

Step 6.2.1.3

Simplify the expression.

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Step 6.2.1.3.1

Multiply $- 2$ by $3$ .

$x = \frac{- 6}{7}$

Step 6.2.1.3.2

Move the negative in front of the fraction.

$x = - \frac{6}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{6}{7}$

Decimal Form:

$x = - 0.\overline{857142}$