Algebra Examples

$4 x - \frac{2}{5} x - (3 x - y) + (\frac{1}{2} x - \frac{1}{5} y - (\frac{1}{6} x - \frac{1}{3} y))$

Step 1

Remove parentheses.

$4 x - \frac{2}{5} x - (3 x - y) + \frac{1}{2} x - \frac{1}{5} y - (\frac{1}{6} x - \frac{1}{3} y)$

Step 2

Simplify each term.

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Step 2.1

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

$4 x - \frac{x \cdot 2}{5} - (3 x - y) + \frac{1}{2} x - \frac{1}{5} y - (\frac{1}{6} x - \frac{1}{3} y)$

Step 2.2

Move $2$ to the left of $x$ .

$4 x - \frac{2 \cdot x}{5} - (3 x - y) + \frac{1}{2} x - \frac{1}{5} y - (\frac{1}{6} x - \frac{1}{3} y)$

Step 2.3

Apply the distributive property.

$4 x - \frac{2 x}{5} - (3 x) - - y + \frac{1}{2} x - \frac{1}{5} y - (\frac{1}{6} x - \frac{1}{3} y)$

Step 2.4

Multiply $3$ by $- 1$ .

$4 x - \frac{2 x}{5} - 3 x - - y + \frac{1}{2} x - \frac{1}{5} y - (\frac{1}{6} x - \frac{1}{3} y)$

Step 2.5

Multiply $- - y$ .

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Step 2.5.1

Multiply $- 1$ by $- 1$ .

$4 x - \frac{2 x}{5} - 3 x + 1 y + \frac{1}{2} x - \frac{1}{5} y - (\frac{1}{6} x - \frac{1}{3} y)$

Step 2.5.2

Multiply $y$ by $1$ .

$4 x - \frac{2 x}{5} - 3 x + y + \frac{1}{2} x - \frac{1}{5} y - (\frac{1}{6} x - \frac{1}{3} y)$

Step 2.6

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

$4 x - \frac{2 x}{5} - 3 x + y + \frac{x}{2} - \frac{1}{5} y - (\frac{1}{6} x - \frac{1}{3} y)$

Step 2.7

Combine $y$ and $\frac{1}{5}$ .

$4 x - \frac{2 x}{5} - 3 x + y + \frac{x}{2} - \frac{y}{5} - (\frac{1}{6} x - \frac{1}{3} y)$

Step 2.8

Simplify each term.

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Step 2.8.1

Combine $\frac{1}{6}$ and $x$ .

$4 x - \frac{2 x}{5} - 3 x + y + \frac{x}{2} - \frac{y}{5} - (\frac{x}{6} - \frac{1}{3} y)$

Step 2.8.2

Combine $y$ and $\frac{1}{3}$ .

$4 x - \frac{2 x}{5} - 3 x + y + \frac{x}{2} - \frac{y}{5} - (\frac{x}{6} - \frac{y}{3})$

Step 2.9

Apply the distributive property.

$4 x - \frac{2 x}{5} - 3 x + y + \frac{x}{2} - \frac{y}{5} - \frac{x}{6} - - \frac{y}{3}$

Step 2.10

Multiply $- - \frac{y}{3}$ .

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Step 2.10.1

Multiply $- 1$ by $- 1$ .

$4 x - \frac{2 x}{5} - 3 x + y + \frac{x}{2} - \frac{y}{5} - \frac{x}{6} + 1 \frac{y}{3}$

Step 2.10.2

Multiply $\frac{y}{3}$ by $1$ .

$4 x - \frac{2 x}{5} - 3 x + y + \frac{x}{2} - \frac{y}{5} - \frac{x}{6} + \frac{y}{3}$

Step 3

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

$4 x \cdot \frac{5}{5} - \frac{2 x}{5} - 3 x + y + \frac{x}{2} - \frac{y}{5} - \frac{x}{6} + \frac{y}{3}$

Step 4

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

$\frac{4 x \cdot 5}{5} - \frac{2 x}{5} - 3 x + y + \frac{x}{2} - \frac{y}{5} - \frac{x}{6} + \frac{y}{3}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 x \cdot 5 - 2 x}{5} - 3 x + y + \frac{x}{2} - \frac{y}{5} - \frac{x}{6} + \frac{y}{3}$

Step 6

Combine the numerators over the common denominator.

$- 3 x + y + \frac{4 x \cdot 5 - 2 x - y}{5} + \frac{x}{2} + \frac{- x}{6} + \frac{y}{3}$

Step 7

Multiply $5$ by $4$ .

$- 3 x + y + \frac{20 x - 2 x - y}{5} + \frac{x}{2} + \frac{- x}{6} + \frac{y}{3}$

Step 8

Subtract $2 x$ from $20 x$ .

$- 3 x + y + \frac{18 x - y}{5} + \frac{x}{2} + \frac{- x}{6} + \frac{y}{3}$

Step 9

Move the negative in front of the fraction.

$- 3 x + y + \frac{18 x - y}{5} + \frac{x}{2} - \frac{x}{6} + \frac{y}{3}$

Step 10

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y - 3 x \cdot \frac{5}{5} + \frac{18 x - y}{5} + \frac{x}{2} - \frac{x}{6} + \frac{y}{3}$

Step 11

Simplify terms.

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Step 11.1

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

$y + \frac{- 3 x \cdot 5}{5} + \frac{18 x - y}{5} + \frac{x}{2} - \frac{x}{6} + \frac{y}{3}$

Step 11.2

Combine the numerators over the common denominator.

$y + \frac{- 3 x \cdot 5 + 18 x - y}{5} + \frac{x}{2} - \frac{x}{6} + \frac{y}{3}$

Step 12

Simplify the numerator.

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Step 12.1

Multiply $5$ by $- 3$ .

$y + \frac{- 15 x + 18 x - y}{5} + \frac{x}{2} - \frac{x}{6} + \frac{y}{3}$

Step 12.2

Add $- 15 x$ and $18 x$ .

$y + \frac{3 x - y}{5} + \frac{x}{2} - \frac{x}{6} + \frac{y}{3}$

Step 13

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

$y \cdot \frac{5}{5} + \frac{3 x - y}{5} + \frac{x}{2} - \frac{x}{6} + \frac{y}{3}$

Step 14

Combine $y$ and $\frac{5}{5}$ .

$\frac{y \cdot 5}{5} + \frac{3 x - y}{5} + \frac{x}{2} - \frac{x}{6} + \frac{y}{3}$

Step 15

Combine the numerators over the common denominator.

$\frac{y \cdot 5 + 3 x - y}{5} + \frac{x}{2} - \frac{x}{6} + \frac{y}{3}$

Step 16

Subtract $y$ from $y \cdot 5$ .

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Step 16.1

Reorder $y$ and $5$ .

$\frac{3 x + 5 \cdot y - y}{5} + \frac{x}{2} - \frac{x}{6} + \frac{y}{3}$

Step 16.2

Subtract $y$ from $5 \cdot y$ .

$\frac{3 x + 4 \cdot y}{5} + \frac{x}{2} - \frac{x}{6} + \frac{y}{3}$

Step 17

To write $\frac{3 x + 4 y}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x + 4 y}{5} \cdot \frac{2}{2} + \frac{x}{2} - \frac{x}{6} + \frac{y}{3}$

Step 18

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

$\frac{3 x + 4 y}{5} \cdot \frac{2}{2} + \frac{x}{2} \cdot \frac{5}{5} - \frac{x}{6} + \frac{y}{3}$

Step 19

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

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Step 19.1

Multiply $\frac{3 x + 4 y}{5}$ by $\frac{2}{2}$ .

$\frac{(3 x + 4 y) \cdot 2}{5 \cdot 2} + \frac{x}{2} \cdot \frac{5}{5} - \frac{x}{6} + \frac{y}{3}$

Step 19.2

Multiply $5$ by $2$ .

$\frac{(3 x + 4 y) \cdot 2}{10} + \frac{x}{2} \cdot \frac{5}{5} - \frac{x}{6} + \frac{y}{3}$

Step 19.3

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

$\frac{(3 x + 4 y) \cdot 2}{10} + \frac{x \cdot 5}{2 \cdot 5} - \frac{x}{6} + \frac{y}{3}$

Step 19.4

Multiply $2$ by $5$ .

$\frac{(3 x + 4 y) \cdot 2}{10} + \frac{x \cdot 5}{10} - \frac{x}{6} + \frac{y}{3}$

Step 20

Combine the numerators over the common denominator.

$\frac{(3 x + 4 y) \cdot 2 + x \cdot 5}{10} - \frac{x}{6} + \frac{y}{3}$

Step 21

Simplify the numerator.

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Step 21.1

Apply the distributive property.

$\frac{3 x \cdot 2 + 4 y \cdot 2 + x \cdot 5}{10} - \frac{x}{6} + \frac{y}{3}$

Step 21.2

Multiply $2$ by $3$ .

$\frac{6 x + 4 y \cdot 2 + x \cdot 5}{10} - \frac{x}{6} + \frac{y}{3}$

Step 21.3

Multiply $2$ by $4$ .

$\frac{6 x + 8 y + x \cdot 5}{10} - \frac{x}{6} + \frac{y}{3}$

Step 21.4

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

$\frac{6 x + 8 y + 5 \cdot x}{10} - \frac{x}{6} + \frac{y}{3}$

Step 21.5

Add $6 x$ and $5 x$ .

$\frac{11 x + 8 y}{10} - \frac{x}{6} + \frac{y}{3}$

Step 22

To write $\frac{11 x + 8 y}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{11 x + 8 y}{10} \cdot \frac{3}{3} - \frac{x}{6} + \frac{y}{3}$

Step 23

To write $- \frac{x}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{11 x + 8 y}{10} \cdot \frac{3}{3} - \frac{x}{6} \cdot \frac{5}{5} + \frac{y}{3}$

Step 24

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 24.1

Multiply $\frac{11 x + 8 y}{10}$ by $\frac{3}{3}$ .

$\frac{(11 x + 8 y) \cdot 3}{10 \cdot 3} - \frac{x}{6} \cdot \frac{5}{5} + \frac{y}{3}$

Step 24.2

Multiply $10$ by $3$ .

$\frac{(11 x + 8 y) \cdot 3}{30} - \frac{x}{6} \cdot \frac{5}{5} + \frac{y}{3}$

Step 24.3

Multiply $\frac{x}{6}$ by $\frac{5}{5}$ .

$\frac{(11 x + 8 y) \cdot 3}{30} - \frac{x \cdot 5}{6 \cdot 5} + \frac{y}{3}$

Step 24.4

Multiply $6$ by $5$ .

$\frac{(11 x + 8 y) \cdot 3}{30} - \frac{x \cdot 5}{30} + \frac{y}{3}$

Step 25

Combine the numerators over the common denominator.

$\frac{(11 x + 8 y) \cdot 3 - x \cdot 5}{30} + \frac{y}{3}$

Step 26

Simplify each term.

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Step 26.1

Simplify the numerator.

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Step 26.1.1

Apply the distributive property.

$\frac{11 x \cdot 3 + 8 y \cdot 3 - x \cdot 5}{30} + \frac{y}{3}$

Step 26.1.2

Multiply $3$ by $11$ .

$\frac{33 x + 8 y \cdot 3 - x \cdot 5}{30} + \frac{y}{3}$

Step 26.1.3

Multiply $3$ by $8$ .

$\frac{33 x + 24 y - x \cdot 5}{30} + \frac{y}{3}$

Step 26.1.4

Multiply $5$ by $- 1$ .

$\frac{33 x + 24 y - 5 x}{30} + \frac{y}{3}$

Step 26.1.5

Subtract $5 x$ from $33 x$ .

$\frac{28 x + 24 y}{30} + \frac{y}{3}$

Step 26.1.6

Factor $4$ out of $28 x + 24 y$ .

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Step 26.1.6.1

Factor $4$ out of $28 x$ .

$\frac{4 (7 x) + 24 y}{30} + \frac{y}{3}$

Step 26.1.6.2

Factor $4$ out of $24 y$ .

$\frac{4 (7 x) + 4 (6 y)}{30} + \frac{y}{3}$

Step 26.1.6.3

Factor $4$ out of $4 (7 x) + 4 (6 y)$ .

$\frac{4 (7 x + 6 y)}{30} + \frac{y}{3}$

Step 26.2

Cancel the common factor of $4$ and $30$ .

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Step 26.2.1

Factor $2$ out of $4 (7 x + 6 y)$ .

$\frac{2 (2 (7 x + 6 y))}{30} + \frac{y}{3}$

Step 26.2.2

Cancel the common factors.

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Step 26.2.2.1

Factor $2$ out of $30$ .

$\frac{2 (2 (7 x + 6 y))}{2 (15)} + \frac{y}{3}$

Step 26.2.2.2

Cancel the common factor.

$\frac{2 (2 (7 x + 6 y))}{2 \cdot 15} + \frac{y}{3}$

Step 26.2.2.3

Rewrite the expression.

$\frac{2 (7 x + 6 y)}{15} + \frac{y}{3}$

Step 27

To write $\frac{y}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 (7 x + 6 y)}{15} + \frac{y}{3} \cdot \frac{5}{5}$

Step 28

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 28.1

Multiply $\frac{y}{3}$ by $\frac{5}{5}$ .

$\frac{2 (7 x + 6 y)}{15} + \frac{y \cdot 5}{3 \cdot 5}$

Step 28.2

Multiply $3$ by $5$ .

$\frac{2 (7 x + 6 y)}{15} + \frac{y \cdot 5}{15}$

Step 29

Combine the numerators over the common denominator.

$\frac{2 (7 x + 6 y) + y \cdot 5}{15}$

Step 30

Simplify the numerator.

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Step 30.1

Apply the distributive property.

$\frac{2 (7 x) + 2 (6 y) + y \cdot 5}{15}$

Step 30.2

Multiply $7$ by $2$ .

$\frac{14 x + 2 (6 y) + y \cdot 5}{15}$

Step 30.3

Multiply $6$ by $2$ .

$\frac{14 x + 12 y + y \cdot 5}{15}$

Step 30.4

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

$\frac{14 x + 12 y + 5 \cdot y}{15}$

Step 30.5

Add $12 y$ and $5 y$ .

$\frac{14 x + 17 y}{15}$