Finite Math Examples

$\frac{4}{5} x - \frac{7}{10} x = 4$

Step 1

Simplify $\frac{4}{5} x - \frac{7}{10} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{4 x}{5} - \frac{7}{10} x = 4$

Step 1.1.2

Combine $x$ and $\frac{7}{10}$ .

$\frac{4 x}{5} - \frac{x \cdot 7}{10} = 4$

Step 1.1.3

Move $7$ to the left of $x$ .

$\frac{4 x}{5} - \frac{7 x}{10} = 4$

Step 1.2

To write $\frac{4 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 x}{5} \cdot \frac{2}{2} - \frac{7 x}{10} = 4$

Step 1.3

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

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Step 1.3.1

Multiply $\frac{4 x}{5}$ by $\frac{2}{2}$ .

$\frac{4 x \cdot 2}{5 \cdot 2} - \frac{7 x}{10} = 4$

Step 1.3.2

Multiply $5$ by $2$ .

$\frac{4 x \cdot 2}{10} - \frac{7 x}{10} = 4$

Step 1.4

Combine the numerators over the common denominator.

$\frac{4 x \cdot 2 - 7 x}{10} = 4$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $x$ out of $4 x \cdot 2 - 7 x$ .

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Step 1.5.1.1

Factor $x$ out of $4 x \cdot 2$ .

$\frac{x (4 \cdot 2) - 7 x}{10} = 4$

Step 1.5.1.2

Factor $x$ out of $- 7 x$ .

$\frac{x (4 \cdot 2) + x \cdot - 7}{10} = 4$

Step 1.5.1.3

Factor $x$ out of $x (4 \cdot 2) + x \cdot - 7$ .

$\frac{x (4 \cdot 2 - 7)}{10} = 4$

Step 1.5.2

Multiply $4$ by $2$ .

$\frac{x (8 - 7)}{10} = 4$

Step 1.5.3

Subtract $7$ from $8$ .

$\frac{x \cdot 1}{10} = 4$

Step 1.6

Multiply $x$ by $1$ .

$\frac{x}{10} = 4$

Step 2

Multiply both sides of the equation by $10$ .

$10 \frac{x}{10} = 10 \cdot 4$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $10$ .

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Step 3.1.1.1

Cancel the common factor.

$10 \frac{x}{10} = 10 \cdot 4$

Step 3.1.1.2

Rewrite the expression.

$x = 10 \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $10$ by $4$ .

$x = 40$