Finite Math Examples

$\frac{x}{2} - 8 = \frac{x}{5}$

Step 1

Multiply both sides by $5$ .

$(\frac{x}{2} - 8) \cdot 5 = \frac{x}{5} \cdot 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{x}{2} - 8) \cdot 5$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Apply the distributive property.

$\frac{x}{2} \cdot 5 - 8 \cdot 5 = \frac{x}{5} \cdot 5$

Step 2.1.1.1.2

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

$\frac{x \cdot 5}{2} - 8 \cdot 5 = \frac{x}{5} \cdot 5$

Step 2.1.1.1.3

Multiply $- 8$ by $5$ .

$\frac{x \cdot 5}{2} - 40 = \frac{x}{5} \cdot 5$

Step 2.1.1.2

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

$\frac{5 x}{2} - 40 = \frac{x}{5} \cdot 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 x}{2} - 40 = \frac{x}{5} \cdot 5$

Step 2.2.1.2

Rewrite the expression.

$\frac{5 x}{2} - 40 = x$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$\frac{5 x}{2} - 40 - x = 0$

Step 3.1.2

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

$\frac{5 x}{2} - x \cdot \frac{2}{2} - 40 = 0$

Step 3.1.3

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

$\frac{5 x}{2} + \frac{- x \cdot 2}{2} - 40 = 0$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{5 x - x \cdot 2}{2} - 40 = 0$

Step 3.1.5

Simplify each term.

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Step 3.1.5.1

Simplify the numerator.

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Step 3.1.5.1.1

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

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Step 3.1.5.1.1.1

Factor $x$ out of $5 x$ .

$\frac{x \cdot 5 - x \cdot 2}{2} - 40 = 0$

Step 3.1.5.1.1.2

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

$\frac{x \cdot 5 + x (- 1 \cdot 2)}{2} - 40 = 0$

Step 3.1.5.1.1.3

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

$\frac{x (5 - 1 \cdot 2)}{2} - 40 = 0$

Step 3.1.5.1.2

Multiply $- 1$ by $2$ .

$\frac{x (5 - 2)}{2} - 40 = 0$

Step 3.1.5.1.3

Subtract $2$ from $5$ .

$\frac{x \cdot 3}{2} - 40 = 0$

Step 3.1.5.2

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

$\frac{3 x}{2} - 40 = 0$

Step 3.2

Add $40$ to both sides of the equation.

$\frac{3 x}{2} = 40$

Step 3.3

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot 40$

Step 3.4

Simplify both sides of the equation.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

Simplify $\frac{2}{3} \cdot \frac{3 x}{2}$ .

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Step 3.4.1.1.1

Cancel the common factor of $2$ .

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Step 3.4.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot 40$

Step 3.4.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot 40$

Step 3.4.1.1.2

Cancel the common factor of $3$ .

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Step 3.4.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{2}{3} \cdot 40$

Step 3.4.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot 40$

Step 3.4.1.1.2.3

Rewrite the expression.

$x = \frac{2}{3} \cdot 40$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Multiply $\frac{2}{3} \cdot 40$ .

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Step 3.4.2.1.1

Combine $\frac{2}{3}$ and $40$ .

$x = \frac{2 \cdot 40}{3}$

Step 3.4.2.1.2

Multiply $2$ by $40$ .

$x = \frac{80}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{80}{3}$

Decimal Form:

$x = 26.\overline{6}$

Mixed Number Form:

$x = 26 \frac{2}{3}$