Basic Math Examples

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

Step 1

Multiply both sides by $2$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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Step 2.2.1.1

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

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

Step 2.2.1.2

Simplify terms.

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Step 2.2.1.2.1

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

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

Step 2.2.1.2.2

Combine the numerators over the common denominator.

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

Step 2.2.1.3

Simplify the numerator.

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Step 2.2.1.3.1

Multiply $3$ by $4$ .

$y + 3 = \frac{y - 5 + 12}{4} \cdot 2$

Step 2.2.1.3.2

Add $- 5$ and $12$ .

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

Step 2.2.1.4

Cancel the common factor of $2$ .

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Step 2.2.1.4.1

Factor $2$ out of $4$ .

$y + 3 = \frac{y + 7}{2 (2)} \cdot 2$

Step 2.2.1.4.2

Cancel the common factor.

$y + 3 = \frac{y + 7}{2 \cdot 2} \cdot 2$

Step 2.2.1.4.3

Rewrite the expression.

$y + 3 = \frac{y + 7}{2}$

Step 3

Solve for $y$ .

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Step 3.1

Multiply both sides by $2$ .

$(y + 3) \cdot 2 = \frac{y + 7}{2} \cdot 2$

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 $(y + 3) \cdot 2$ .

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Step 3.2.1.1.1

Apply the distributive property.

$y \cdot 2 + 3 \cdot 2 = \frac{y + 7}{2} \cdot 2$

Step 3.2.1.1.2

Simplify the expression.

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Step 3.2.1.1.2.1

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

$2 \cdot y + 3 \cdot 2 = \frac{y + 7}{2} \cdot 2$

Step 3.2.1.1.2.2

Multiply $3$ by $2$ .

$2 y + 6 = \frac{y + 7}{2} \cdot 2$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$2 y + 6 = \frac{y + 7}{2} \cdot 2$

Step 3.2.2.1.2

Rewrite the expression.

$2 y + 6 = y + 7$

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 $y$ from both sides of the equation.

$2 y + 6 - y = 7$

Step 3.3.1.2

Subtract $y$ from $2 y$ .

$y + 6 = 7$

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

Subtract $6$ from both sides of the equation.

$y = 7 - 6$

Step 3.3.2.2

Subtract $6$ from $7$ .

$y = 1$