Algebra Examples

$20 (\frac{3}{5} y - 2 - \frac{3}{2} y) = 2 + 2 y$

Step 1

Simplify $20 (\frac{3}{5} y - 2 - \frac{3}{2} y)$ .

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Step 1.1

Rewrite.

$0 + 0 + 20 (\frac{3}{5} y - 2 - \frac{3}{2} y) = 2 + 2 y$

Step 1.2

Simplify by adding zeros.

$20 (\frac{3}{5} y - 2 - \frac{3}{2} y) = 2 + 2 y$

Step 1.3

Simplify each term.

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Step 1.3.1

Combine $\frac{3}{5}$ and $y$ .

$20 (\frac{3 y}{5} - 2 - \frac{3}{2} y) = 2 + 2 y$

Step 1.3.2

Combine $y$ and $\frac{3}{2}$ .

$20 (\frac{3 y}{5} - 2 - \frac{y \cdot 3}{2}) = 2 + 2 y$

Step 1.3.3

Move $3$ to the left of $y$ .

$20 (\frac{3 y}{5} - 2 - \frac{3 y}{2}) = 2 + 2 y$

Step 1.4

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

$20 (\frac{3 y}{5} \cdot \frac{2}{2} - \frac{3 y}{2} - 2) = 2 + 2 y$

Step 1.5

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

$20 (\frac{3 y}{5} \cdot \frac{2}{2} - \frac{3 y}{2} \cdot \frac{5}{5} - 2) = 2 + 2 y$

Step 1.6

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

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Step 1.6.1

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

$20 (\frac{3 y \cdot 2}{5 \cdot 2} - \frac{3 y}{2} \cdot \frac{5}{5} - 2) = 2 + 2 y$

Step 1.6.2

Multiply $5$ by $2$ .

$20 (\frac{3 y \cdot 2}{10} - \frac{3 y}{2} \cdot \frac{5}{5} - 2) = 2 + 2 y$

Step 1.6.3

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

$20 (\frac{3 y \cdot 2}{10} - \frac{3 y \cdot 5}{2 \cdot 5} - 2) = 2 + 2 y$

Step 1.6.4

Multiply $2$ by $5$ .

$20 (\frac{3 y \cdot 2}{10} - \frac{3 y \cdot 5}{10} - 2) = 2 + 2 y$

Step 1.7

Combine the numerators over the common denominator.

$20 (\frac{3 y \cdot 2 - 3 y \cdot 5}{10} - 2) = 2 + 2 y$

Step 1.8

Simplify each term.

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Step 1.8.1

Simplify the numerator.

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Step 1.8.1.1

Factor $3 y$ out of $3 y \cdot 2 - 3 y \cdot 5$ .

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Step 1.8.1.1.1

Factor $3 y$ out of $3 y \cdot 2$ .

$20 (\frac{3 y (2) - 3 y \cdot 5}{10} - 2) = 2 + 2 y$

Step 1.8.1.1.2

Factor $3 y$ out of $- 3 y \cdot 5$ .

$20 (\frac{3 y (2) + 3 y (- 1 \cdot 5)}{10} - 2) = 2 + 2 y$

Step 1.8.1.1.3

Factor $3 y$ out of $3 y (2) + 3 y (- 1 \cdot 5)$ .

$20 (\frac{3 y (2 - 1 \cdot 5)}{10} - 2) = 2 + 2 y$

Step 1.8.1.2

Multiply $- 1$ by $5$ .

$20 (\frac{3 y (2 - 5)}{10} - 2) = 2 + 2 y$

Step 1.8.1.3

Subtract $5$ from $2$ .

$20 (\frac{3 y \cdot - 3}{10} - 2) = 2 + 2 y$

Step 1.8.1.4

Multiply $- 3$ by $3$ .

$20 (\frac{- 9 y}{10} - 2) = 2 + 2 y$

Step 1.8.2

Move the negative in front of the fraction.

$20 (- \frac{9 y}{10} - 2) = 2 + 2 y$

Step 1.9

Simplify terms.

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Step 1.9.1

Apply the distributive property.

$20 (- \frac{9 y}{10}) + 20 \cdot - 2 = 2 + 2 y$

Step 1.9.2

Cancel the common factor of $10$ .

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Step 1.9.2.1

Move the leading negative in $- \frac{9 y}{10}$ into the numerator.

$20 \frac{- 9 y}{10} + 20 \cdot - 2 = 2 + 2 y$

Step 1.9.2.2

Factor $10$ out of $20$ .

$10 (2) \frac{- 9 y}{10} + 20 \cdot - 2 = 2 + 2 y$

Step 1.9.2.3

Cancel the common factor.

$10 \cdot 2 \frac{- 9 y}{10} + 20 \cdot - 2 = 2 + 2 y$

Step 1.9.2.4

Rewrite the expression.

$2 (- 9 y) + 20 \cdot - 2 = 2 + 2 y$

Step 1.9.3

Multiply.

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Step 1.9.3.1

Multiply $- 9$ by $2$ .

$- 18 y + 20 \cdot - 2 = 2 + 2 y$

Step 1.9.3.2

Multiply $20$ by $- 2$ .

$- 18 y - 40 = 2 + 2 y$

Step 2

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

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Step 2.1

Subtract $2 y$ from both sides of the equation.

$- 18 y - 40 - 2 y = 2$

Step 2.2

Subtract $2 y$ from $- 18 y$ .

$- 20 y - 40 = 2$

Step 3

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

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Step 3.1

Add $40$ to both sides of the equation.

$- 20 y = 2 + 40$

Step 3.2

Add $2$ and $40$ .

$- 20 y = 42$

Step 4

Divide each term in $- 20 y = 42$ by $- 20$ and simplify.

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Step 4.1

Divide each term in $- 20 y = 42$ by $- 20$ .

$\frac{- 20 y}{- 20} = \frac{42}{- 20}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 20$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 20 y}{- 20} = \frac{42}{- 20}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{42}{- 20}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $42$ and $- 20$ .

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Step 4.3.1.1

Factor $2$ out of $42$ .

$y = \frac{2 (21)}{- 20}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $2$ out of $- 20$ .

$y = \frac{2 \cdot 21}{2 \cdot - 10}$

Step 4.3.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 21}{2 \cdot - 10}$

Step 4.3.1.2.3

Rewrite the expression.

$y = \frac{21}{- 10}$

Step 4.3.2

Move the negative in front of the fraction.

$y = - \frac{21}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{21}{10}$

Decimal Form:

$y = - 2.1$

Mixed Number Form:

$y = - 2 \frac{1}{10}$