Finite Math Examples

$\frac{7 x}{5} - \frac{5}{10} x = x - \frac{7}{2}$

Step 1

Simplify $\frac{7 x}{5} - \frac{5}{10} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Cancel the common factor of $5$ and $10$ .

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Step 1.1.1.1

Factor $5$ out of $5$ .

$\frac{7 x}{5} - \frac{5 (1)}{10} x = x - \frac{7}{2}$

Step 1.1.1.2

Cancel the common factors.

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Step 1.1.1.2.1

Factor $5$ out of $10$ .

$\frac{7 x}{5} - \frac{5 \cdot 1}{5 \cdot 2} x = x - \frac{7}{2}$

Step 1.1.1.2.2

Cancel the common factor.

$\frac{7 x}{5} - \frac{5 \cdot 1}{5 \cdot 2} x = x - \frac{7}{2}$

Step 1.1.1.2.3

Rewrite the expression.

$\frac{7 x}{5} - \frac{1}{2} x = x - \frac{7}{2}$

Step 1.1.2

Combine $x$ and $\frac{1}{2}$ .

$\frac{7 x}{5} - \frac{x}{2} = x - \frac{7}{2}$

Step 1.2

To write $\frac{7 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 x}{5} \cdot \frac{2}{2} - \frac{x}{2} = x - \frac{7}{2}$

Step 1.3

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

$\frac{7 x}{5} \cdot \frac{2}{2} - \frac{x}{2} \cdot \frac{5}{5} = x - \frac{7}{2}$

Step 1.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{7 x}{5}$ by $\frac{2}{2}$ .

$\frac{7 x \cdot 2}{5 \cdot 2} - \frac{x}{2} \cdot \frac{5}{5} = x - \frac{7}{2}$

Step 1.4.2

Multiply $5$ by $2$ .

$\frac{7 x \cdot 2}{10} - \frac{x}{2} \cdot \frac{5}{5} = x - \frac{7}{2}$

Step 1.4.3

Multiply $\frac{x}{2}$ by $\frac{5}{5}$ .

$\frac{7 x \cdot 2}{10} - \frac{x \cdot 5}{2 \cdot 5} = x - \frac{7}{2}$

Step 1.4.4

Multiply $2$ by $5$ .

$\frac{7 x \cdot 2}{10} - \frac{x \cdot 5}{10} = x - \frac{7}{2}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{7 x \cdot 2 - x \cdot 5}{10} = x - \frac{7}{2}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Factor $x$ out of $7 x \cdot 2 - x \cdot 5$ .

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Step 1.6.1.1

Factor $x$ out of $7 x \cdot 2$ .

$\frac{x (7 \cdot 2) - x \cdot 5}{10} = x - \frac{7}{2}$

Step 1.6.1.2

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

$\frac{x (7 \cdot 2) + x (- 1 \cdot 5)}{10} = x - \frac{7}{2}$

Step 1.6.1.3

Factor $x$ out of $x (7 \cdot 2) + x (- 1 \cdot 5)$ .

$\frac{x (7 \cdot 2 - 1 \cdot 5)}{10} = x - \frac{7}{2}$

Step 1.6.2

Multiply $7$ by $2$ .

$\frac{x (14 - 1 \cdot 5)}{10} = x - \frac{7}{2}$

Step 1.6.3

Multiply $- 1$ by $5$ .

$\frac{x (14 - 5)}{10} = x - \frac{7}{2}$

Step 1.6.4

Subtract $5$ from $14$ .

$\frac{x \cdot 9}{10} = x - \frac{7}{2}$

Step 1.7

Move $9$ to the left of $x$ .

$\frac{9 x}{10} = x - \frac{7}{2}$

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$\frac{9 x}{10} - x = - \frac{7}{2}$

Step 2.2

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

$\frac{9 x}{10} - x \cdot \frac{10}{10} = - \frac{7}{2}$

Step 2.3

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

$\frac{9 x}{10} + \frac{- x \cdot 10}{10} = - \frac{7}{2}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{9 x - x \cdot 10}{10} = - \frac{7}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Factor $x$ out of $9 x - x \cdot 10$ .

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Step 2.5.1.1

Factor $x$ out of $9 x$ .

$\frac{x \cdot 9 - x \cdot 10}{10} = - \frac{7}{2}$

Step 2.5.1.2

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

$\frac{x \cdot 9 + x (- 1 \cdot 10)}{10} = - \frac{7}{2}$

Step 2.5.1.3

Factor $x$ out of $x \cdot 9 + x (- 1 \cdot 10)$ .

$\frac{x (9 - 1 \cdot 10)}{10} = - \frac{7}{2}$

Step 2.5.2

Multiply $- 1$ by $10$ .

$\frac{x (9 - 10)}{10} = - \frac{7}{2}$

Step 2.5.3

Subtract $10$ from $9$ .

$\frac{x \cdot - 1}{10} = - \frac{7}{2}$

Step 2.6

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{10} = - \frac{7}{2}$

Step 2.7

Move the negative in front of the fraction.

$- \frac{x}{10} = - \frac{7}{2}$

Step 3

Multiply both sides of the equation by $- 10$ .

$- 10 (- \frac{x}{10}) = - 10 (- \frac{7}{2})$

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 $- 10 (- \frac{x}{10})$ .

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Step 4.1.1.1

Cancel the common factor of $10$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{x}{10}$ into the numerator.

$- 10 \frac{- x}{10} = - 10 (- \frac{7}{2})$

Step 4.1.1.1.2

Factor $10$ out of $- 10$ .

$10 (- 1) \frac{- x}{10} = - 10 (- \frac{7}{2})$

Step 4.1.1.1.3

Cancel the common factor.

$10 \cdot - 1 \frac{- x}{10} = - 10 (- \frac{7}{2})$

Step 4.1.1.1.4

Rewrite the expression.

$- - x = - 10 (- \frac{7}{2})$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 10 (- \frac{7}{2})$

Step 4.1.1.2.2

Multiply $x$ by $1$ .

$x = - 10 (- \frac{7}{2})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 10 (- \frac{7}{2})$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$x = - 10 (\frac{- 7}{2})$

Step 4.2.1.1.2

Factor $2$ out of $- 10$ .

$x = 2 (- 5) \frac{- 7}{2}$

Step 4.2.1.1.3

Cancel the common factor.

$x = 2 \cdot - 5 \frac{- 7}{2}$

Step 4.2.1.1.4

Rewrite the expression.

$x = - 5 \cdot - 7$

Step 4.2.1.2

Multiply $- 5$ by $- 7$ .

$x = 35$