Basic Math Examples

$- 5 (3 y - 5) = 3 (4 - 5)$

Step 1

Simplify.

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Step 1.1

Subtract $5$ from $4$ .

$- 5 (3 y - 5) = 3 \cdot - 1$

Step 1.2

Multiply $3$ by $- 1$ .

$- 5 (3 y - 5) = - 3$

Step 2

Divide each term in $- 5 (3 y - 5) = - 3$ by $- 5$ and simplify.

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Step 2.1

Divide each term in $- 5 (3 y - 5) = - 3$ by $- 5$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 5$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $3 y - 5$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Dividing two negative values results in a positive value.

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

Step 3

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

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Step 3.1

Add $5$ to both sides of the equation.

$3 y = \frac{3}{5} + 5$

Step 3.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$3 y = \frac{3}{5} + 5 \cdot \frac{5}{5}$

Step 3.3

Combine $5$ and $\frac{5}{5}$ .

$3 y = \frac{3}{5} + \frac{5 \cdot 5}{5}$

Step 3.4

Combine the numerators over the common denominator.

$3 y = \frac{3 + 5 \cdot 5}{5}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $5$ by $5$ .

$3 y = \frac{3 + 25}{5}$

Step 3.5.2

Add $3$ and $25$ .

$3 y = \frac{28}{5}$

Step 4

Divide each term in $3 y = \frac{28}{5}$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 y = \frac{28}{5}$ by $3$ .

$\frac{3 y}{3} = \frac{\frac{28}{5}}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{\frac{28}{5}}{3}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{28}{5}}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{28}{5} \cdot \frac{1}{3}$

Step 4.3.2

Multiply $\frac{28}{5} \cdot \frac{1}{3}$ .

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Step 4.3.2.1

Multiply $\frac{28}{5}$ by $\frac{1}{3}$ .

$y = \frac{28}{5 \cdot 3}$

Step 4.3.2.2

Multiply $5$ by $3$ .

$y = \frac{28}{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{28}{15}$

Decimal Form:

$y = 1.8\overline{6}$

Mixed Number Form:

$y = 1 \frac{13}{15}$