Algebra Examples

$\frac{2}{3} b + 5 = 20 - b$

Step 1

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

$\frac{2 b}{3} + 5 = 20 - b$

Step 2

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

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Step 2.1

Add $b$ to both sides of the equation.

$\frac{2 b}{3} + 5 + b = 20$

Step 2.2

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

$\frac{2 b}{3} + b \cdot \frac{3}{3} + 5 = 20$

Step 2.3

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

$\frac{2 b}{3} + \frac{b \cdot 3}{3} + 5 = 20$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 b + b \cdot 3}{3} + 5 = 20$

Step 2.5

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

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Step 2.5.1

Reorder $b$ and $3$ .

$\frac{2 b + 3 \cdot b}{3} + 5 = 20$

Step 2.5.2

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

$\frac{5 b}{3} + 5 = 20$

Step 3

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

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Step 3.1

Subtract $5$ from both sides of the equation.

$\frac{5 b}{3} = 20 - 5$

Step 3.2

Subtract $5$ from $20$ .

$\frac{5 b}{3} = 15$

Step 4

Multiply both sides of the equation by $\frac{3}{5}$ .

$\frac{3}{5} \cdot \frac{5 b}{3} = \frac{3}{5} \cdot 15$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{3}{5} \cdot \frac{5 b}{3}$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{3}{5} \cdot \frac{5 b}{3} = \frac{3}{5} \cdot 15$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 b) = \frac{3}{5} \cdot 15$

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $5 b$ .

$\frac{1}{5} (5 (b)) = \frac{3}{5} \cdot 15$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 b) = \frac{3}{5} \cdot 15$

Step 5.1.1.2.3

Rewrite the expression.

$b = \frac{3}{5} \cdot 15$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{3}{5} \cdot 15$ .

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Step 5.2.1.1

Cancel the common factor of $5$ .

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Step 5.2.1.1.1

Factor $5$ out of $15$ .

$b = \frac{3}{5} \cdot (5 (3))$

Step 5.2.1.1.2

Cancel the common factor.

$b = \frac{3}{5} \cdot (5 \cdot 3)$

Step 5.2.1.1.3

Rewrite the expression.

$b = 3 \cdot 3$

Step 5.2.1.2

Multiply $3$ by $3$ .

$b = 9$