Basic Math Examples

$\frac{2 y - 3}{6} - \frac{3 y - 1}{2} = \frac{10 - 3 y}{4}$

Step 1

Multiply both sides by $4$ .

$(\frac{2 y - 3}{6} - \frac{3 y - 1}{2}) \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{2 y - 3}{6} - \frac{3 y - 1}{2}) \cdot 4$ .

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Step 2.1.1.1

To write $- \frac{3 y - 1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{2 y - 3}{6} - \frac{3 y - 1}{2} \cdot \frac{3}{3}) \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.1.2.1

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

$(\frac{2 y - 3}{6} - \frac{(3 y - 1) \cdot 3}{2 \cdot 3}) \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.2.2

Multiply $2$ by $3$ .

$(\frac{2 y - 3}{6} - \frac{(3 y - 1) \cdot 3}{6}) \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.3

Combine the numerators over the common denominator.

$\frac{2 y - 3 - (3 y - 1) \cdot 3}{6} \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.4

Simplify the numerator.

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Step 2.1.1.4.1

Apply the distributive property.

$\frac{2 y - 3 + (- (3 y) - - 1) \cdot 3}{6} \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.4.2

Multiply $3$ by $- 1$ .

$\frac{2 y - 3 + (- 3 y - - 1) \cdot 3}{6} \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.4.3

Multiply $- 1$ by $- 1$ .

$\frac{2 y - 3 + (- 3 y + 1) \cdot 3}{6} \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.4.4

Apply the distributive property.

$\frac{2 y - 3 - 3 y \cdot 3 + 1 \cdot 3}{6} \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.4.5

Multiply $3$ by $- 3$ .

$\frac{2 y - 3 - 9 y + 1 \cdot 3}{6} \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.4.6

Multiply $3$ by $1$ .

$\frac{2 y - 3 - 9 y + 3}{6} \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.4.7

Subtract $9 y$ from $2 y$ .

$\frac{- 7 y - 3 + 3}{6} \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.4.8

Add $- 3$ and $3$ .

$\frac{- 7 y + 0}{6} \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.4.9

Add $- 7 y$ and $0$ .

$\frac{- 7 y}{6} \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.5

Simplify terms.

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Step 2.1.1.5.1

Cancel the common factor of $2$ .

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Step 2.1.1.5.1.1

Factor $2$ out of $6$ .

$\frac{- 7 y}{2 (3)} \cdot 4 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.5.1.2

Factor $2$ out of $4$ .

$\frac{- 7 y}{2 \cdot 3} \cdot (2 \cdot 2) = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.5.1.3

Cancel the common factor.

$\frac{- 7 y}{2 \cdot 3} \cdot (2 \cdot 2) = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.5.1.4

Rewrite the expression.

$\frac{- 7 y}{3} \cdot 2 = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.5.2

Combine $\frac{- 7 y}{3}$ and $2$ .

$\frac{- 7 y \cdot 2}{3} = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.5.3

Simplify the expression.

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Step 2.1.1.5.3.1

Multiply $2$ by $- 7$ .

$\frac{- 14 y}{3} = \frac{10 - 3 y}{4} \cdot 4$

Step 2.1.1.5.3.2

Move the negative in front of the fraction.

$- \frac{14 y}{3} = \frac{10 - 3 y}{4} \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{10 - 3 y}{4} \cdot 4$ .

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Step 2.2.1.1

Cancel the common factor of $4$ .

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Step 2.2.1.1.1

Cancel the common factor.

$- \frac{14 y}{3} = \frac{10 - 3 y}{4} \cdot 4$

Step 2.2.1.1.2

Rewrite the expression.

$- \frac{14 y}{3} = 10 - 3 y$

Step 2.2.1.2

Reorder $10$ and $- 3 y$ .

$- \frac{14 y}{3} = - 3 y + 10$

Step 3

Solve for $y$ .

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Step 3.1

Multiply both sides by $3$ .

$- \frac{14 y}{3} \cdot 3 = (- 3 y + 10) \cdot 3$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{14 y}{3}$ into the numerator.

$\frac{- 14 y}{3} \cdot 3 = (- 3 y + 10) \cdot 3$

Step 3.2.1.1.2

Cancel the common factor.

$\frac{- 14 y}{3} \cdot 3 = (- 3 y + 10) \cdot 3$

Step 3.2.1.1.3

Rewrite the expression.

$- 14 y = (- 3 y + 10) \cdot 3$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(- 3 y + 10) \cdot 3$ .

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Step 3.2.2.1.1

Apply the distributive property.

$- 14 y = - 3 y \cdot 3 + 10 \cdot 3$

Step 3.2.2.1.2

Multiply.

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Step 3.2.2.1.2.1

Multiply $3$ by $- 3$ .

$- 14 y = - 9 y + 10 \cdot 3$

Step 3.2.2.1.2.2

Multiply $10$ by $3$ .

$- 14 y = - 9 y + 30$

Step 3.3

Solve for $y$ .

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Step 3.3.1

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

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Step 3.3.1.1

Add $9 y$ to both sides of the equation.

$- 14 y + 9 y = 30$

Step 3.3.1.2

Add $- 14 y$ and $9 y$ .

$- 5 y = 30$

Step 3.3.2

Divide each term in $- 5 y = 30$ by $- 5$ and simplify.

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Step 3.3.2.1

Divide each term in $- 5 y = 30$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{30}{- 5}$

Step 3.3.2.2

Simplify the left side.

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Step 3.3.2.2.1

Cancel the common factor of $- 5$ .

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Step 3.3.2.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{30}{- 5}$

Step 3.3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{30}{- 5}$

Step 3.3.2.3

Simplify the right side.

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Step 3.3.2.3.1

Divide $30$ by $- 5$ .

$y = - 6$