Algebra Examples

$4 = \frac{12 b + 8}{b + 24}$

Step 1

Rewrite the equation as $\frac{12 b + 8}{b + 24} = 4$ .

$\frac{12 b + 8}{b + 24} = 4$

Step 2

Factor $4$ out of $12 b + 8$ .

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Step 2.1

Factor $4$ out of $12 b$ .

$\frac{4 (3 b) + 8}{b + 24} = 4$

Step 2.2

Factor $4$ out of $8$ .

$\frac{4 (3 b) + 4 (2)}{b + 24} = 4$

Step 2.3

Factor $4$ out of $4 (3 b) + 4 (2)$ .

$\frac{4 (3 b + 2)}{b + 24} = 4$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$b + 24, 1$

Step 3.2

Remove parentheses.

$b + 24, 1$

Step 3.3

The LCM of one and any expression is the expression.

$b + 24$

Step 4

Multiply each term in $\frac{4 (3 b + 2)}{b + 24} = 4$ by $b + 24$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{4 (3 b + 2)}{b + 24} = 4$ by $b + 24$ .

$\frac{4 (3 b + 2)}{b + 24} (b + 24) = 4 (b + 24)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $b + 24$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 (3 b + 2)}{b + 24} (b + 24) = 4 (b + 24)$

Step 4.2.1.2

Rewrite the expression.

$4 (3 b + 2) = 4 (b + 24)$

Step 4.2.2

Apply the distributive property.

$4 (3 b) + 4 \cdot 2 = 4 (b + 24)$

Step 4.2.3

Multiply.

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Step 4.2.3.1

Multiply $3$ by $4$ .

$12 b + 4 \cdot 2 = 4 (b + 24)$

Step 4.2.3.2

Multiply $4$ by $2$ .

$12 b + 8 = 4 (b + 24)$

Step 4.3

Simplify the right side.

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Step 4.3.1

Apply the distributive property.

$12 b + 8 = 4 b + 4 \cdot 24$

Step 4.3.2

Multiply $4$ by $24$ .

$12 b + 8 = 4 b + 96$

Step 5

Solve the equation.

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Step 5.1

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

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Step 5.1.1

Subtract $4 b$ from both sides of the equation.

$12 b + 8 - 4 b = 96$

Step 5.1.2

Subtract $4 b$ from $12 b$ .

$8 b + 8 = 96$

Step 5.2

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

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Step 5.2.1

Subtract $8$ from both sides of the equation.

$8 b = 96 - 8$

Step 5.2.2

Subtract $8$ from $96$ .

$8 b = 88$

Step 5.3

Divide each term in $8 b = 88$ by $8$ and simplify.

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Step 5.3.1

Divide each term in $8 b = 88$ by $8$ .

$\frac{8 b}{8} = \frac{88}{8}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $8$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{8 b}{8} = \frac{88}{8}$

Step 5.3.2.1.2

Divide $b$ by $1$ .

$b = \frac{88}{8}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Divide $88$ by $8$ .

$b = 11$