Algebra Examples

$2 x + \frac{1}{5} - x + \frac{2}{5} = 4 x - \frac{2}{5}$

Step 1

Simplify $2 x + \frac{1}{5} - x + \frac{2}{5}$ .

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Step 1.1

Combine the numerators over the common denominator.

$2 x - x + \frac{1 + 2}{5} = 4 x - \frac{2}{5}$

Step 1.2

Add $1$ and $2$ .

$2 x - x + \frac{3}{5} = 4 x - \frac{2}{5}$

Step 1.3

Subtract $x$ from $2 x$ .

$x + \frac{3}{5} = 4 x - \frac{2}{5}$

Step 2

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

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Step 2.1

Subtract $4 x$ from both sides of the equation.

$x + \frac{3}{5} - 4 x = - \frac{2}{5}$

Step 2.2

Subtract $4 x$ from $x$ .

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

Step 3

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

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Step 3.1

Subtract $\frac{3}{5}$ from both sides of the equation.

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Subtract $3$ from $- 2$ .

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

Step 3.4

Divide $- 5$ by $5$ .

$- 3 x = - 1$

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

Dividing two negative values results in a positive value.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{3}$