Basic Math Examples

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

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

Step 1

Subtract

31

$31$ from both sides of the equation.

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

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

Step 2

Simplify

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

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

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Step 2.1

Combine

\frac{2}{3}

$\frac{2}{3}$ and

y

$y$ .

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

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

Step 2.2

To write

y

$y$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 2.3

Combine

y

$y$ and

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 2.4

Combine the numerators over the common denominator.

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

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

Step 2.5

Add

2 y

$2 y$ and

y \cdot 3

$y \cdot 3$ .

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Step 2.5.1

Reorder

y

$y$ and

3

$3$ .

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

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

Step 2.5.2

Add

2 y

$2 y$ and

3 \cdot y

$3 \cdot y$ .

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

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

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

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

Step 2.6

Subtract

31

$31$ from

- 4

$- 4$ .

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

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

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

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

Step 3

Factor the left side.

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Step 3.1

Factor

5

$5$ out of

\frac{5 y}{3} - 35

$\frac{5 y}{3} - 35$ .

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Step 3.1.1

Factor

5

$5$ out of

\frac{5 y}{3}

$\frac{5 y}{3}$ .

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

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

Step 3.1.2

Factor

5

$5$ out of

- 35

$- 35$ .

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

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

Step 3.1.3

Factor

5

$5$ out of

5 \frac{y}{3} + 5 \cdot - 7

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

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

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

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

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

Step 3.2

To write

- 7

$- 7$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 3.3

Combine

- 7

$- 7$ and

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 3.4

Combine the numerators over the common denominator.

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

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

Step 3.5

Multiply

- 7

$- 7$ by

3

$3$ .

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

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

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

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