Algebra Examples

$3 = \frac{3}{4} (b - 8)$

Step 1

Rewrite the equation as $\frac{3}{4} \cdot (b - 8) = 3$ .

$\frac{3}{4} \cdot (b - 8) = 3$

Step 2

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} (\frac{3}{4} \cdot (b - 8)) = \frac{4}{3} \cdot 3$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{4}{3} (\frac{3}{4} \cdot (b - 8))$ .

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Step 3.1.1.1

Apply the distributive property.

$\frac{4}{3} (\frac{3}{4} b + \frac{3}{4} \cdot - 8) = \frac{4}{3} \cdot 3$

Step 3.1.1.2

Combine $\frac{3}{4}$ and $b$ .

$\frac{4}{3} (\frac{3 b}{4} + \frac{3}{4} \cdot - 8) = \frac{4}{3} \cdot 3$

Step 3.1.1.3

Cancel the common factor of $4$ .

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Step 3.1.1.3.1

Factor $4$ out of $- 8$ .

$\frac{4}{3} (\frac{3 b}{4} + \frac{3}{4} \cdot (4 (- 2))) = \frac{4}{3} \cdot 3$

Step 3.1.1.3.2

Cancel the common factor.

$\frac{4}{3} (\frac{3 b}{4} + \frac{3}{4} \cdot (4 \cdot - 2)) = \frac{4}{3} \cdot 3$

Step 3.1.1.3.3

Rewrite the expression.

$\frac{4}{3} (\frac{3 b}{4} + 3 \cdot - 2) = \frac{4}{3} \cdot 3$

Step 3.1.1.4

Multiply $3$ by $- 2$ .

$\frac{4}{3} (\frac{3 b}{4} - 6) = \frac{4}{3} \cdot 3$

Step 3.1.1.5

Apply the distributive property.

$\frac{4}{3} \cdot \frac{3 b}{4} + \frac{4}{3} \cdot - 6 = \frac{4}{3} \cdot 3$

Step 3.1.1.6

Cancel the common factor of $4$ .

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Step 3.1.1.6.1

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 b}{4} + \frac{4}{3} \cdot - 6 = \frac{4}{3} \cdot 3$

Step 3.1.1.6.2

Rewrite the expression.

$\frac{1}{3} (3 b) + \frac{4}{3} \cdot - 6 = \frac{4}{3} \cdot 3$

Step 3.1.1.7

Cancel the common factor of $3$ .

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Step 3.1.1.7.1

Factor $3$ out of $3 b$ .

$\frac{1}{3} (3 (b)) + \frac{4}{3} \cdot - 6 = \frac{4}{3} \cdot 3$

Step 3.1.1.7.2

Cancel the common factor.

$\frac{1}{3} (3 b) + \frac{4}{3} \cdot - 6 = \frac{4}{3} \cdot 3$

Step 3.1.1.7.3

Rewrite the expression.

$b + \frac{4}{3} \cdot - 6 = \frac{4}{3} \cdot 3$

Step 3.1.1.8

Cancel the common factor of $3$ .

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Step 3.1.1.8.1

Factor $3$ out of $- 6$ .

$b + \frac{4}{3} \cdot (3 (- 2)) = \frac{4}{3} \cdot 3$

Step 3.1.1.8.2

Cancel the common factor.

$b + \frac{4}{3} \cdot (3 \cdot - 2) = \frac{4}{3} \cdot 3$

Step 3.1.1.8.3

Rewrite the expression.

$b + 4 \cdot - 2 = \frac{4}{3} \cdot 3$

Step 3.1.1.9

Multiply $4$ by $- 2$ .

$b - 8 = \frac{4}{3} \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$b - 8 = \frac{4}{3} \cdot 3$

Step 3.2.1.2

Rewrite the expression.

$b - 8 = 4$

Step 4

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

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Step 4.1

Add $8$ to both sides of the equation.

$b = 4 + 8$

Step 4.2

Add $4$ and $8$ .

$b = 12$