Basic Math Examples

$\frac{7}{2} y + \frac{9}{6} = 3 y - 7$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{7 y}{2} + \frac{9}{6} = 3 y - 7$

Step 1.2

Cancel the common factor of $9$ and $6$ .

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Step 1.2.1

Factor $3$ out of $9$ .

$\frac{7 y}{2} + \frac{3 (3)}{6} = 3 y - 7$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3$ out of $6$ .

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Combine the numerators over the common denominator.

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

Step 2.6

Multiply $2$ by $- 3$ .

$\frac{7 y - 6 y + 3}{2} = - 7$

Step 2.7

Subtract $6 y$ from $7 y$ .

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

Step 3

Multiply both sides of the equation by $2$ .

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

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

Cancel the common factor of $2$ .

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Step 4.1.1.1

Cancel the common factor.

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

Step 4.1.1.2

Rewrite the expression.

$y + 3 = 2 \cdot - 7$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $2$ by $- 7$ .

$y + 3 = - 14$

Step 5

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

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Step 5.1

Subtract $3$ from both sides of the equation.

$y = - 14 - 3$

Step 5.2

Subtract $3$ from $- 14$ .

$y = - 17$