Algebra Examples

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

Step 1

Simplify $- \frac{x}{5} - \frac{2}{5} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $x$ and $\frac{2}{5}$ .

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

Step 1.1.2

Move $2$ to the left of $x$ .

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

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

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

Step 1.2.2

Subtract $2 x$ from $- x$ .

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

Step 1.2.3

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- \frac{5}{3} (- \frac{3 x}{5})$ .

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Step 3.1.1.1

Cancel the common factor of $5$ .

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Step 3.1.1.1.1

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

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

Step 3.1.1.1.2

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

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

Step 3.1.1.1.3

Factor $5$ out of $- 5$ .

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

Step 3.1.1.1.4

Cancel the common factor.

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

Step 3.1.1.1.5

Rewrite the expression.

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

Step 3.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.2.1

Factor $3$ out of $- 3 x$ .

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

Step 3.1.1.2.2

Cancel the common factor.

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

Step 3.1.1.2.3

Rewrite the expression.

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

Step 3.1.1.3

Multiply.

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Step 3.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.1.3.2

Multiply $x$ by $1$ .

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{5}{3} \cdot 2$ .

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Step 3.2.1.1

Multiply $- \frac{5}{3} \cdot 2$ .

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Step 3.2.1.1.1

Multiply $2$ by $- 1$ .

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

Step 3.2.1.1.2

Combine $- 2$ and $\frac{5}{3}$ .

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

Step 3.2.1.1.3

Multiply $- 2$ by $5$ .

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

Step 3.2.1.2

Move the negative in front of the fraction.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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

Mixed Number Form:

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