Basic Math Examples

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

Step 1

Multiply both sides by $4$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2.1.1.2

Simplify terms.

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Step 2.1.1.2.1

Combine $- 4$ and $\frac{3}{3}$ .

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

Step 2.1.1.2.2

Combine the numerators over the common denominator.

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

Step 2.1.1.3

Simplify the numerator.

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Step 2.1.1.3.1

Multiply $- 4$ by $3$ .

$\frac{y - 2 - 12}{3} \cdot 4 = \frac{y + 1}{4} \cdot 4$

Step 2.1.1.3.2

Subtract $12$ from $- 2$ .

$\frac{y - 14}{3} \cdot 4 = \frac{y + 1}{4} \cdot 4$

Step 2.1.1.4

Combine fractions.

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Step 2.1.1.4.1

Combine $\frac{y - 14}{3}$ and $4$ .

$\frac{(y - 14) \cdot 4}{3} = \frac{y + 1}{4} \cdot 4$

Step 2.1.1.4.2

Move $4$ to the left of $y - 14$ .

$\frac{4 (y - 14)}{3} = \frac{y + 1}{4} \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 (y - 14)}{3} = \frac{y + 1}{4} \cdot 4$

Step 2.2.1.2

Rewrite the expression.

$\frac{4 (y - 14)}{3} = y + 1$

Step 3

Solve for $y$ .

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Step 3.1

Multiply both sides by $3$ .

$\frac{4 (y - 14)}{3} \cdot 3 = (y + 1) \cdot 3$

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

Simplify $\frac{4 (y - 14)}{3} \cdot 3$ .

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Step 3.2.1.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1.1

Cancel the common factor.

$\frac{4 (y - 14)}{3} \cdot 3 = (y + 1) \cdot 3$

Step 3.2.1.1.1.2

Rewrite the expression.

$4 (y - 14) = (y + 1) \cdot 3$

Step 3.2.1.1.2

Apply the distributive property.

$4 y + 4 \cdot - 14 = (y + 1) \cdot 3$

Step 3.2.1.1.3

Multiply $4$ by $- 14$ .

$4 y - 56 = (y + 1) \cdot 3$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(y + 1) \cdot 3$ .

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Step 3.2.2.1.1

Apply the distributive property.

$4 y - 56 = y \cdot 3 + 1 \cdot 3$

Step 3.2.2.1.2

Simplify the expression.

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Step 3.2.2.1.2.1

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

$4 y - 56 = 3 \cdot y + 1 \cdot 3$

Step 3.2.2.1.2.2

Multiply $3$ by $1$ .

$4 y - 56 = 3 y + 3$

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

Subtract $3 y$ from both sides of the equation.

$4 y - 56 - 3 y = 3$

Step 3.3.1.2

Subtract $3 y$ from $4 y$ .

$y - 56 = 3$

Step 3.3.2

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

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Step 3.3.2.1

Add $56$ to both sides of the equation.

$y = 3 + 56$

Step 3.3.2.2

Add $3$ and $56$ .

$y = 59$