Algebra Examples

$5 x - \frac{5}{2} (x - 2) = 10$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$5 x - \frac{5}{2} x - \frac{5}{2} \cdot - 2 = 10$

Step 1.1.2

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

$5 x - \frac{x \cdot 5}{2} - \frac{5}{2} \cdot - 2 = 10$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$5 x - \frac{x \cdot 5}{2} + \frac{- 5}{2} \cdot - 2 = 10$

Step 1.1.3.2

Factor $2$ out of $- 2$ .

$5 x - \frac{x \cdot 5}{2} + \frac{- 5}{2} \cdot (2 (- 1)) = 10$

Step 1.1.3.3

Cancel the common factor.

$5 x - \frac{x \cdot 5}{2} + \frac{- 5}{2} \cdot (2 \cdot - 1) = 10$

Step 1.1.3.4

Rewrite the expression.

$5 x - \frac{x \cdot 5}{2} - 5 \cdot - 1 = 10$

Step 1.1.4

Multiply $- 5$ by $- 1$ .

$5 x - \frac{x \cdot 5}{2} + 5 = 10$

Step 1.1.5

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

$5 x - \frac{5 x}{2} + 5 = 10$

Step 1.2

To write $5 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 x \cdot \frac{2}{2} - \frac{5 x}{2} + 5 = 10$

Step 1.3

Simplify terms.

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Step 1.3.1

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

$\frac{5 x \cdot 2}{2} - \frac{5 x}{2} + 5 = 10$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{5 x \cdot 2 - 5 x}{2} + 5 = 10$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $5 x$ out of $5 x \cdot 2 - 5 x$ .

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Step 1.4.1.1

Factor $5 x$ out of $5 x \cdot 2$ .

$\frac{5 x (2) - 5 x}{2} + 5 = 10$

Step 1.4.1.2

Factor $5 x$ out of $- 5 x$ .

$\frac{5 x (2) + 5 x (- 1)}{2} + 5 = 10$

Step 1.4.1.3

Factor $5 x$ out of $5 x (2) + 5 x (- 1)$ .

$\frac{5 x (2 - 1)}{2} + 5 = 10$

Step 1.4.2

Subtract $1$ from $2$ .

$\frac{5 x \cdot 1}{2} + 5 = 10$

Step 1.4.3

Multiply $5$ by $1$ .

$\frac{5 x}{2} + 5 = 10$

Step 2

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

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Step 2.1

Subtract $5$ from both sides of the equation.

$\frac{5 x}{2} = 10 - 5$

Step 2.2

Subtract $5$ from $10$ .

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

Step 3

Multiply both sides of the equation by $\frac{2}{5}$ .

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Cancel the common factor.

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

Step 4.1.1.1.2

Rewrite the expression.

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

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Factor $5$ out of $5 x$ .

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

Step 4.1.1.2.2

Cancel the common factor.

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

Step 4.1.1.2.3

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Rewrite the expression.

$x = 2$