Basic Math Examples

$\frac{2}{3} y + y - 4 = 31$

Step 1

Subtract $31$ from both sides of the equation.

$\frac{2}{3} y + y - 4 - 31 = 0$

Step 2

Simplify $\frac{2}{3} y + y - 4 - 31$ .

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Step 2.1

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

$\frac{2 y}{3} + y - 4 - 31 = 0$

Step 2.2

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

$\frac{2 y}{3} + y \cdot \frac{3}{3} - 4 - 31 = 0$

Step 2.3

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

$\frac{2 y}{3} + \frac{y \cdot 3}{3} - 4 - 31 = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 y + y \cdot 3}{3} - 4 - 31 = 0$

Step 2.5

Add $2 y$ and $y \cdot 3$ .

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Step 2.5.1

Reorder $y$ and $3$ .

$\frac{2 y + 3 \cdot y}{3} - 4 - 31 = 0$

Step 2.5.2

Add $2 y$ and $3 \cdot y$ .

$\frac{5 y}{3} - 4 - 31 = 0$

Step 2.6

Subtract $31$ from $- 4$ .

$\frac{5 y}{3} - 35 = 0$

Step 3

Factor the left side.

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Step 3.1

Factor $5$ out of $\frac{5 y}{3} - 35$ .

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Step 3.1.1

Factor $5$ out of $\frac{5 y}{3}$ .

$5 \frac{y}{3} - 35 = 0$

Step 3.1.2

Factor $5$ out of $- 35$ .

$5 \frac{y}{3} + 5 \cdot - 7 = 0$

Step 3.1.3

Factor $5$ out of $5 \frac{y}{3} + 5 \cdot - 7$ .

$5 (\frac{y}{3} - 7) = 0$

Step 3.2

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$5 (\frac{y}{3} - 7 \cdot \frac{3}{3}) = 0$

Step 3.3

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

$5 (\frac{y}{3} + \frac{- 7 \cdot 3}{3}) = 0$

Step 3.4

Combine the numerators over the common denominator.

$5 \frac{y - 7 \cdot 3}{3} = 0$

Step 3.5

Multiply $- 7$ by $3$ .

$5 \frac{y - 21}{3} = 0$