Precalculus Examples

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

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

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Subtract $\frac{1}{5}$ from both sides of the equation.

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

Simplify the right side of the equation.

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Combine the numerators over the common denominator.

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

Subtract $1$ from $2$ .

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

Multiply both sides of the equation by $- \frac{5}{3}$ .

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

Simplify both sides of the equation.

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Simplify the left side.

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Cancel the common factor of $5$ .

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Move the leading negative in $- \frac{5}{3}$ into the numerator.

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

Move the leading negative in $- \frac{3 x}{5}$ into the numerator.

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

Factor out the greatest common factor $5$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

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Factor out the greatest common factor $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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Multiply $\frac{- 1}{1}$ and $\frac{- x}{1}$ .

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

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Divide $x$ by $1$ .

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

Simplify $- \frac{5}{3} \cdot \frac{1}{5}$ .

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Cancel the common factor of $5$ .

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Move the leading negative in $- \frac{5}{3}$ into the numerator.

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

Factor out the greatest common factor $5$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{- 1}{3} \cdot \frac{1}{1}$

Simplify.

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Multiply $\frac{- 1}{3}$ and $\frac{1}{1}$ .

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

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.\overline{3}$

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