Basic Math Examples

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

Step 1

Simplify $\frac{4 y}{3} + 2 (3 - y)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Multiply $2$ by $3$ .

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

Step 1.1.3

Multiply $- 1$ by $2$ .

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

Step 1.2

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

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

Step 1.3

Simplify terms.

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Step 1.3.1

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

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

Step 1.3.2

Combine the numerators over the common denominator.

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

Step 1.4

Simplify each term.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Factor $2 y$ out of $4 y - 2 y \cdot 3$ .

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Step 1.4.1.1.1

Factor $2 y$ out of $4 y$ .

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

Step 1.4.1.1.2

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

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

Step 1.4.1.1.3

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

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

Step 1.4.1.2

Multiply $- 1$ by $3$ .

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

Step 1.4.1.3

Subtract $3$ from $2$ .

$\frac{2 y \cdot - 1}{3} + 6 = 5$

Step 1.4.1.4

Multiply $- 1$ by $2$ .

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

Step 1.4.2

Move the negative in front of the fraction.

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

Step 2

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

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Step 2.1

Subtract $6$ from both sides of the equation.

$- \frac{2 y}{3} = 5 - 6$

Step 2.2

Subtract $6$ from $5$ .

$- \frac{2 y}{3} = - 1$

Step 3

Multiply both sides of the equation by $- \frac{3}{2}$ .

$- \frac{3}{2} (- \frac{2 y}{3}) = - \frac{3}{2} \cdot - 1$

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

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{- 3}{2} (- \frac{2 y}{3}) = - \frac{3}{2} \cdot - 1$

Step 4.1.1.1.2

Move the leading negative in $- \frac{2 y}{3}$ into the numerator.

$\frac{- 3}{2} \cdot \frac{- 2 y}{3} = - \frac{3}{2} \cdot - 1$

Step 4.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{2} \cdot \frac{- 2 y}{3} = - \frac{3}{2} \cdot - 1$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{- 2 y}{3} = - \frac{3}{2} \cdot - 1$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} (- 2 y) = - \frac{3}{2} \cdot - 1$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Factor $2$ out of $- 2 y$ .

$\frac{- 1}{2} (2 (- y)) = - \frac{3}{2} \cdot - 1$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} (2 (- y)) = - \frac{3}{2} \cdot - 1$

Step 4.1.1.2.3

Rewrite the expression.

$- - y = - \frac{3}{2} \cdot - 1$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{3}{2} \cdot - 1$

Step 4.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{3}{2} \cdot - 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- \frac{3}{2} \cdot - 1$ .

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Step 4.2.1.1

Multiply $- 1$ by $- 1$ .

$y = 1 (\frac{3}{2})$

Step 4.2.1.2

Multiply $\frac{3}{2}$ by $1$ .

$y = \frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{3}{2}$

Decimal Form:

$y = 1.5$

Mixed Number Form:

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