Algebra Examples

$\frac{7 + 8 y}{15} - \frac{8}{3} = \frac{2 y}{5}$

Step 1

Multiply both sides by $5$ .

$(\frac{7 + 8 y}{15} - \frac{8}{3}) \cdot 5 = \frac{2 y}{5} \cdot 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{7 + 8 y}{15} - \frac{8}{3}) \cdot 5$ .

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Step 2.1.1.1

To write $- \frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{7 + 8 y}{15} - \frac{8}{3} \cdot \frac{5}{5}) \cdot 5 = \frac{2 y}{5} \cdot 5$

Step 2.1.1.2

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.1.2.1

Multiply $\frac{8}{3}$ by $\frac{5}{5}$ .

$(\frac{7 + 8 y}{15} - \frac{8 \cdot 5}{3 \cdot 5}) \cdot 5 = \frac{2 y}{5} \cdot 5$

Step 2.1.1.2.2

Multiply $3$ by $5$ .

$(\frac{7 + 8 y}{15} - \frac{8 \cdot 5}{15}) \cdot 5 = \frac{2 y}{5} \cdot 5$

Step 2.1.1.3

Combine the numerators over the common denominator.

$\frac{7 + 8 y - 8 \cdot 5}{15} \cdot 5 = \frac{2 y}{5} \cdot 5$

Step 2.1.1.4

Simplify the numerator.

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Step 2.1.1.4.1

Multiply $- 8$ by $5$ .

$\frac{7 + 8 y - 40}{15} \cdot 5 = \frac{2 y}{5} \cdot 5$

Step 2.1.1.4.2

Subtract $40$ from $7$ .

$\frac{8 y - 33}{15} \cdot 5 = \frac{2 y}{5} \cdot 5$

Step 2.1.1.5

Cancel the common factor of $5$ .

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Step 2.1.1.5.1

Factor $5$ out of $15$ .

$\frac{8 y - 33}{5 (3)} \cdot 5 = \frac{2 y}{5} \cdot 5$

Step 2.1.1.5.2

Cancel the common factor.

$\frac{8 y - 33}{5 \cdot 3} \cdot 5 = \frac{2 y}{5} \cdot 5$

Step 2.1.1.5.3

Rewrite the expression.

$\frac{8 y - 33}{3} = \frac{2 y}{5} \cdot 5$

Step 2.2

Simplify the right 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.

$\frac{8 y - 33}{3} = \frac{2 y}{5} \cdot 5$

Step 2.2.1.2

Rewrite the expression.

$\frac{8 y - 33}{3} = 2 y$

Step 3

Solve for $y$ .

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Step 3.1

Multiply both sides by $3$ .

$\frac{8 y - 33}{3} \cdot 3 = 2 y \cdot 3$

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

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Cancel the common factor.

$\frac{8 y - 33}{3} \cdot 3 = 2 y \cdot 3$

Step 3.2.1.1.2

Rewrite the expression.

$8 y - 33 = 2 y \cdot 3$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $3$ by $2$ .

$8 y - 33 = 6 y$

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 $6 y$ from both sides of the equation.

$8 y - 33 - 6 y = 0$

Step 3.3.1.2

Subtract $6 y$ from $8 y$ .

$2 y - 33 = 0$

Step 3.3.2

Add $33$ to both sides of the equation.

$2 y = 33$

Step 3.3.3

Divide each term in $2 y = 33$ by $2$ and simplify.

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Step 3.3.3.1

Divide each term in $2 y = 33$ by $2$ .

$\frac{2 y}{2} = \frac{33}{2}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $2$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{33}{2}$

Step 3.3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{33}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{33}{2}$

Decimal Form:

$y = 16.5$

Mixed Number Form:

$y = 16 \frac{1}{2}$