Pre-Algebra Examples

$\frac{2}{5} \cdot (3 x + 5) - \frac{1}{5} x = \frac{4}{5} x + 1$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{2}{5} (3 x) + \frac{2}{5} \cdot 5 - \frac{1}{5} x = \frac{4}{5} x + 1$

Step 1.1.2

Multiply $\frac{2}{5} (3 x)$ .

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Step 1.1.2.1

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

$\frac{3 \cdot 2}{5} x + \frac{2}{5} \cdot 5 - \frac{1}{5} x = \frac{4}{5} x + 1$

Step 1.1.2.2

Multiply $3$ by $2$ .

$\frac{6}{5} x + \frac{2}{5} \cdot 5 - \frac{1}{5} x = \frac{4}{5} x + 1$

Step 1.1.2.3

Combine $\frac{6}{5}$ and $x$ .

$\frac{6 x}{5} + \frac{2}{5} \cdot 5 - \frac{1}{5} x = \frac{4}{5} x + 1$

Step 1.1.3

Cancel the common factor of $5$ .

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Step 1.1.3.1

Cancel the common factor.

$\frac{6 x}{5} + \frac{2}{5} \cdot 5 - \frac{1}{5} x = \frac{4}{5} x + 1$

Step 1.1.3.2

Rewrite the expression.

$\frac{6 x}{5} + 2 - \frac{1}{5} x = \frac{4}{5} x + 1$

Step 1.1.4

Combine $x$ and $\frac{1}{5}$ .

$\frac{6 x}{5} + 2 - \frac{x}{5} = \frac{4}{5} x + 1$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$2 + \frac{6 x - x}{5} = \frac{4}{5} x + 1$

Step 1.2.2

Subtract $x$ from $6 x$ .

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

Step 1.2.3

Cancel the common factor of $5$ .

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Step 1.2.3.1

Cancel the common factor.

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

Step 1.2.3.2

Divide $x$ by $1$ .

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

Step 2

Combine $\frac{4}{5}$ and $x$ .

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

Step 3

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

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Step 3.1

Subtract $\frac{4 x}{5}$ from both sides of the equation.

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Subtract $4 x$ from $x \cdot 5$ .

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Step 3.5.1

Reorder $x$ and $5$ .

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

Step 3.5.2

Subtract $4 x$ from $5 \cdot x$ .

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

Step 4

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

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Step 4.1

Subtract $2$ from both sides of the equation.

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

Step 4.2

Subtract $2$ from $1$ .

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

Step 5

Multiply both sides of the equation by $5$ .

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

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $5$ .

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Step 6.1.1.1

Cancel the common factor.

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

Step 6.1.1.2

Rewrite the expression.

$x = 5 \cdot - 1$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $5$ by $- 1$ .

$x = - 5$