Algebra Examples

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

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

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

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

Step 1.1.3

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

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Step 1.1.3.1

Multiply $- 3$ by $- 1$ .

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

Step 1.1.3.2

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

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

Step 1.1.3.3

Multiply $3$ by $2$ .

$x - \frac{x \cdot 2}{5} + \frac{6}{5} - \frac{1}{5} = - \frac{3}{5} x$

Step 1.1.4

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

$x - \frac{2 x}{5} + \frac{6}{5} - \frac{1}{5} = - \frac{3}{5} x$

Step 1.2

Combine fractions.

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Step 1.2.1

Combine the numerators over the common denominator.

$x + \frac{- 2 x + 6 - 1}{5} = - \frac{3}{5} x$

Step 1.2.2

Subtract $1$ from $6$ .

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

Step 1.3

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

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

Step 1.4

Simplify terms.

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Step 1.4.1

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

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

Step 1.4.2

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Move $5$ to the left of $x$ .

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

Step 1.5.2

Subtract $2 x$ from $5 x$ .

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

Step 2

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

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Step 2.1

Combine $x$ and $\frac{3}{5}$ .

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

Step 2.2

Move $3$ to the left of $x$ .

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

Step 3

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

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Step 3.1

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

$\frac{3 x + 5}{5} + \frac{3 x}{5} = 0$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3 x + 5 + 3 x}{5} = 0$

Step 3.3

Add $3 x$ and $3 x$ .

$\frac{6 x + 5}{5} = 0$

Step 4

Set the numerator equal to zero.

$6 x + 5 = 0$

Step 5

Solve the equation for $x$ .

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Step 5.1

Subtract $5$ from both sides of the equation.

$6 x = - 5$

Step 5.2

Divide each term in $6 x = - 5$ by $6$ and simplify.

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Step 5.2.1

Divide each term in $6 x = - 5$ by $6$ .

$\frac{6 x}{6} = \frac{- 5}{6}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $6$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 5}{6}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5}{6}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Move the negative in front of the fraction.

$x = - \frac{5}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{5}{6}$

Decimal Form:

$x = - 0.8\overline{3}$