Precalculus Examples Rational Expressions and Equations

Solve for x

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Subtract $1$ from $2$ .

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

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 3 x = 1$

Step 4

Divide each term in $- 3 x = 1$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 x = 1$ by $- 3$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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

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