Algebra Examples

$3 (\frac{7}{5} x + 4) - 2 (\frac{3}{2} - \frac{5}{4} x)$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{7}{5}$ and $x$ .

$3 (\frac{7 x}{5} + 4) - 2 (\frac{3}{2} - \frac{5}{4} x)$

Step 1.2

Apply the distributive property.

$3 \frac{7 x}{5} + 3 \cdot 4 - 2 (\frac{3}{2} - \frac{5}{4} x)$

Step 1.3

Multiply $3 \frac{7 x}{5}$ .

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Step 1.3.1

Combine $3$ and $\frac{7 x}{5}$ .

$\frac{3 (7 x)}{5} + 3 \cdot 4 - 2 (\frac{3}{2} - \frac{5}{4} x)$

Step 1.3.2

Multiply $7$ by $3$ .

$\frac{21 x}{5} + 3 \cdot 4 - 2 (\frac{3}{2} - \frac{5}{4} x)$

Step 1.4

Multiply $3$ by $4$ .

$\frac{21 x}{5} + 12 - 2 (\frac{3}{2} - \frac{5}{4} x)$

Step 1.5

Simplify each term.

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Step 1.5.1

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

$\frac{21 x}{5} + 12 - 2 (\frac{3}{2} - \frac{x \cdot 5}{4})$

Step 1.5.2

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

$\frac{21 x}{5} + 12 - 2 (\frac{3}{2} - \frac{5 x}{4})$

Step 1.6

Apply the distributive property.

$\frac{21 x}{5} + 12 - 2 (\frac{3}{2}) - 2 (- \frac{5 x}{4})$

Step 1.7

Cancel the common factor of $2$ .

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Step 1.7.1

Factor $2$ out of $- 2$ .

$\frac{21 x}{5} + 12 + 2 (- 1) \frac{3}{2} - 2 (- \frac{5 x}{4})$

Step 1.7.2

Cancel the common factor.

$\frac{21 x}{5} + 12 + 2 \cdot - 1 \frac{3}{2} - 2 (- \frac{5 x}{4})$

Step 1.7.3

Rewrite the expression.

$\frac{21 x}{5} + 12 - 1 \cdot 3 - 2 (- \frac{5 x}{4})$

Step 1.8

Multiply $- 1$ by $3$ .

$\frac{21 x}{5} + 12 - 3 - 2 (- \frac{5 x}{4})$

Step 1.9

Cancel the common factor of $2$ .

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Step 1.9.1

Move the leading negative in $- \frac{5 x}{4}$ into the numerator.

$\frac{21 x}{5} + 12 - 3 - 2 \frac{- 5 x}{4}$

Step 1.9.2

Factor $2$ out of $- 2$ .

$\frac{21 x}{5} + 12 - 3 + 2 (- 1) \frac{- 5 x}{4}$

Step 1.9.3

Factor $2$ out of $4$ .

$\frac{21 x}{5} + 12 - 3 + 2 \cdot - 1 \frac{- 5 x}{2 \cdot 2}$

Step 1.9.4

Cancel the common factor.

$\frac{21 x}{5} + 12 - 3 + 2 \cdot - 1 \frac{- 5 x}{2 \cdot 2}$

Step 1.9.5

Rewrite the expression.

$\frac{21 x}{5} + 12 - 3 - 1 \frac{- 5 x}{2}$

Step 1.10

Simplify each term.

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Step 1.10.1

Move the negative in front of the fraction.

$\frac{21 x}{5} + 12 - 3 - 1 (- \frac{5 x}{2})$

Step 1.10.2

Multiply $- 1 (- \frac{5 x}{2})$ .

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Step 1.10.2.1

Multiply $- 1$ by $- 1$ .

$\frac{21 x}{5} + 12 - 3 + 1 \frac{5 x}{2}$

Step 1.10.2.2

Multiply $\frac{5 x}{2}$ by $1$ .

$\frac{21 x}{5} + 12 - 3 + \frac{5 x}{2}$

Step 2

To write $\frac{21 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{21 x}{5} \cdot \frac{2}{2} + \frac{5 x}{2} + 12 - 3$

Step 3

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

$\frac{21 x}{5} \cdot \frac{2}{2} + \frac{5 x}{2} \cdot \frac{5}{5} + 12 - 3$

Step 4

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

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Step 4.1

Multiply $\frac{21 x}{5}$ by $\frac{2}{2}$ .

$\frac{21 x \cdot 2}{5 \cdot 2} + \frac{5 x}{2} \cdot \frac{5}{5} + 12 - 3$

Step 4.2

Multiply $5$ by $2$ .

$\frac{21 x \cdot 2}{10} + \frac{5 x}{2} \cdot \frac{5}{5} + 12 - 3$

Step 4.3

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

$\frac{21 x \cdot 2}{10} + \frac{5 x \cdot 5}{2 \cdot 5} + 12 - 3$

Step 4.4

Multiply $2$ by $5$ .

$\frac{21 x \cdot 2}{10} + \frac{5 x \cdot 5}{10} + 12 - 3$

Step 5

Combine the numerators over the common denominator.

$\frac{21 x \cdot 2 + 5 x \cdot 5}{10} + 12 - 3$

Step 6

Find the common denominator.

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Step 6.1

Write $12$ as a fraction with denominator $1$ .

$\frac{21 x \cdot 2 + 5 x \cdot 5}{10} + \frac{12}{1} - 3$

Step 6.2

Multiply $\frac{12}{1}$ by $\frac{10}{10}$ .

$\frac{21 x \cdot 2 + 5 x \cdot 5}{10} + \frac{12}{1} \cdot \frac{10}{10} - 3$

Step 6.3

Multiply $\frac{12}{1}$ by $\frac{10}{10}$ .

$\frac{21 x \cdot 2 + 5 x \cdot 5}{10} + \frac{12 \cdot 10}{10} - 3$

Step 6.4

Write $- 3$ as a fraction with denominator $1$ .

$\frac{21 x \cdot 2 + 5 x \cdot 5}{10} + \frac{12 \cdot 10}{10} + \frac{- 3}{1}$

Step 6.5

Multiply $\frac{- 3}{1}$ by $\frac{10}{10}$ .

$\frac{21 x \cdot 2 + 5 x \cdot 5}{10} + \frac{12 \cdot 10}{10} + \frac{- 3}{1} \cdot \frac{10}{10}$

Step 6.6

Multiply $\frac{- 3}{1}$ by $\frac{10}{10}$ .

$\frac{21 x \cdot 2 + 5 x \cdot 5}{10} + \frac{12 \cdot 10}{10} + \frac{- 3 \cdot 10}{10}$

Step 7

Combine the numerators over the common denominator.

$\frac{21 x \cdot 2 + 5 x \cdot 5 + 12 \cdot 10 - 3 \cdot 10}{10}$

Step 8

Simplify each term.

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Step 8.1

Multiply $2$ by $21$ .

$\frac{42 x + 5 x \cdot 5 + 12 \cdot 10 - 3 \cdot 10}{10}$

Step 8.2

Multiply $5$ by $5$ .

$\frac{42 x + 25 x + 12 \cdot 10 - 3 \cdot 10}{10}$

Step 8.3

Multiply $12$ by $10$ .

$\frac{42 x + 25 x + 120 - 3 \cdot 10}{10}$

Step 8.4

Multiply $- 3$ by $10$ .

$\frac{42 x + 25 x + 120 - 30}{10}$

Step 9

Simplify by adding terms.

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Step 9.1

Add $42 x$ and $25 x$ .

$\frac{67 x + 120 - 30}{10}$

Step 9.2

Subtract $30$ from $120$ .

$\frac{67 x + 90}{10}$