Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Subtract $\frac{7 y}{3}$ from both sides of the equation.

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

Step 2.2

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

$5 y \cdot \frac{3}{3} - \frac{7 y}{3} = 8$

Step 2.3

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

$\frac{5 y \cdot 3}{3} - \frac{7 y}{3} = 8$

Step 2.4

Combine the numerators over the common denominator.

$\frac{5 y \cdot 3 - 7 y}{3} = 8$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Factor $y$ out of $5 y \cdot 3 - 7 y$ .

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Step 2.5.1.1

Factor $y$ out of $5 y \cdot 3$ .

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

Step 2.5.1.2

Factor $y$ out of $- 7 y$ .

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

Step 2.5.1.3

Factor $y$ out of $y (5 \cdot 3) + y \cdot - 7$ .

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

Step 2.5.2

Multiply $5$ by $3$ .

$\frac{y (15 - 7)}{3} = 8$

Step 2.5.3

Subtract $7$ from $15$ .

$\frac{y \cdot 8}{3} = 8$

Step 2.6

Move $8$ to the left of $y$ .

$\frac{8 y}{3} = 8$

Step 3

Multiply both sides of the equation by $\frac{3}{8}$ .

$\frac{3}{8} \cdot \frac{8 y}{3} = \frac{3}{8} \cdot 8$

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

Simplify $\frac{3}{8} \cdot \frac{8 y}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{3}{8} \cdot \frac{8 y}{3} = \frac{3}{8} \cdot 8$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{8} (8 y) = \frac{3}{8} \cdot 8$

Step 4.1.1.2

Cancel the common factor of $8$ .

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Step 4.1.1.2.1

Factor $8$ out of $8 y$ .

$\frac{1}{8} (8 (y)) = \frac{3}{8} \cdot 8$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{8} (8 y) = \frac{3}{8} \cdot 8$

Step 4.1.1.2.3

Rewrite the expression.

$y = \frac{3}{8} \cdot 8$

Step 4.2

Simplify the right side.

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Step 4.2.1

Cancel the common factor of $8$ .

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Step 4.2.1.1

Cancel the common factor.

$y = \frac{3}{8} \cdot 8$

Step 4.2.1.2

Rewrite the expression.

$y = 3$