Finite Math Examples

$\frac{8 - 0.1 x}{0.2} = 50 - x$

Step 1

Multiply both sides by $0.2$ .

$\frac{8 - 0.1 x}{0.2} \cdot 0.2 = (50 - x) \cdot 0.2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{8 - 0.1 x}{0.2} \cdot 0.2$ .

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Step 2.1.1.1

Factor $0.1$ out of $8 - 0.1 x$ .

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Step 2.1.1.1.1

Factor $0.1$ out of $8$ .

$\frac{0.1 (80) - 0.1 x}{0.2} \cdot 0.2 = (50 - x) \cdot 0.2$

Step 2.1.1.1.2

Factor $0.1$ out of $- 0.1 x$ .

$\frac{0.1 (80) + 0.1 (- x)}{0.2} \cdot 0.2 = (50 - x) \cdot 0.2$

Step 2.1.1.1.3

Factor $0.1$ out of $0.1 (80) + 0.1 (- x)$ .

$\frac{0.1 (80 - x)}{0.2} \cdot 0.2 = (50 - x) \cdot 0.2$

Step 2.1.1.2

Cancel the common factor of $0.1$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{0.1 (80 - x)}{0.2} \cdot 0.2 = (50 - x) \cdot 0.2$

Step 2.1.1.2.2

Rewrite the expression.

$\frac{80 - x}{0.2} \cdot \frac{0.2}{10} = (50 - x) \cdot 0.2$

Step 2.1.1.3

Cancel the common factor of $0.2$ .

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Step 2.1.1.3.1

Cancel the common factor.

$\frac{80 - x}{0.2} \cdot \frac{0.2}{10} = (50 - x) \cdot 0.2$

Step 2.1.1.3.2

Rewrite the expression.

$(80 - x) \cdot \frac{1}{10} = (50 - x) \cdot 0.2$

Step 2.1.1.4

Apply the distributive property.

$80 (\frac{1}{10}) - x \frac{1}{10} = (50 - x) \cdot 0.2$

Step 2.1.1.5

Cancel the common factor of $10$ .

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Step 2.1.1.5.1

Factor $10$ out of $80$ .

$10 (8) \frac{1}{10} - x \frac{1}{10} = (50 - x) \cdot 0.2$

Step 2.1.1.5.2

Cancel the common factor.

$10 \cdot 8 \frac{1}{10} - x \frac{1}{10} = (50 - x) \cdot 0.2$

Step 2.1.1.5.3

Rewrite the expression.

$8 - x \frac{1}{10} = (50 - x) \cdot 0.2$

Step 2.1.1.6

Combine $\frac{1}{10}$ and $x$ .

$8 - \frac{x}{10} = (50 - x) \cdot 0.2$

Step 2.1.1.7

Reorder $8$ and $- \frac{x}{10}$ .

$- \frac{x}{10} + 8 = (50 - x) \cdot 0.2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(50 - x) \cdot 0.2$ .

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Step 2.2.1.1

Apply the distributive property.

$- \frac{x}{10} + 8 = 50 \cdot 0.2 - x \cdot 0.2$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Multiply $50$ by $0.2$ .

$- \frac{x}{10} + 8 = 10 - x \cdot 0.2$

Step 2.2.1.2.2

Multiply $0.2$ by $- 1$ .

$- \frac{x}{10} + 8 = 10 - 0.2 x$

Step 2.2.1.2.3

Reorder $10$ and $- 0.2 x$ .

$- \frac{x}{10} + 8 = - 0.2 x + 10$

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

Add $0.2 x$ to both sides of the equation.

$- \frac{x}{10} + 8 + 0.2 x = 10$

Step 3.1.2

To write $0.2 x$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$- \frac{x}{10} + 0.2 x \cdot \frac{10}{10} + 8 = 10$

Step 3.1.3

Combine $0.2 x$ and $\frac{10}{10}$ .

$- \frac{x}{10} + \frac{0.2 x \cdot 10}{10} + 8 = 10$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{- x + 0.2 x \cdot 10}{10} + 8 = 10$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Factor $0.2 x$ out of $- x + 0.2 x \cdot 10$ .

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Step 3.1.5.1.1

Move $x$ .

$\frac{- x + 0.2 \cdot 10 x}{10} + 8 = 10$

Step 3.1.5.1.2

Factor $0.2 x$ out of $- x$ .

$\frac{0.2 x (- 5) + 0.2 \cdot 10 x}{10} + 8 = 10$

Step 3.1.5.1.3

Factor $0.2 x$ out of $0.2 \cdot 10 x$ .

$\frac{0.2 x (- 5) + 0.2 x (10)}{10} + 8 = 10$

Step 3.1.5.1.4

Factor $0.2 x$ out of $0.2 x (- 5) + 0.2 x (10)$ .

$\frac{0.2 x (- 5 + 10)}{10} + 8 = 10$

Step 3.1.5.2

Combine exponents.

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Step 3.1.5.2.1

Multiply $- 5 + 10$ by $0.2$ .

$\frac{1 x}{10} + 8 = 10$

Step 3.1.5.2.2

Multiply $x$ by $1$ .

$\frac{x}{10} + 8 = 10$

Step 3.2

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

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Step 3.2.1

Subtract $8$ from both sides of the equation.

$\frac{x}{10} = 10 - 8$

Step 3.2.2

Subtract $8$ from $10$ .

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

Step 3.3

Multiply both sides of the equation by $10$ .

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

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

Cancel the common factor of $10$ .

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Step 3.4.1.1.1

Cancel the common factor.

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

Step 3.4.1.1.2

Rewrite the expression.

$x = 10 \cdot 2$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Multiply $10$ by $2$ .

$x = 20$