Algebra Examples

$\frac{7}{b + 5} = \frac{10}{5}$

Step 1

Subtract $\frac{10}{5}$ from both sides of the equation.

$\frac{7}{b + 5} - \frac{10}{5} = 0$

Step 2

Simplify $\frac{7}{b + 5} - \frac{10}{5}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Divide $10$ by $5$ .

$\frac{7}{b + 5} - 1 \cdot 2 = 0$

Step 2.1.2

Multiply $- 1$ by $2$ .

$\frac{7}{b + 5} - 2 = 0$

Step 2.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{b + 5}{b + 5}$ .

$\frac{7}{b + 5} - 2 \cdot \frac{b + 5}{b + 5} = 0$

Step 2.3

Combine $- 2$ and $\frac{b + 5}{b + 5}$ .

$\frac{7}{b + 5} + \frac{- 2 (b + 5)}{b + 5} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 - 2 (b + 5)}{b + 5} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Apply the distributive property.

$\frac{7 - 2 b - 2 \cdot 5}{b + 5} = 0$

Step 2.5.2

Multiply $- 2$ by $5$ .

$\frac{7 - 2 b - 10}{b + 5} = 0$

Step 2.5.3

Subtract $10$ from $7$ .

$\frac{- 2 b - 3}{b + 5} = 0$

Step 2.6

Factor $- 1$ out of $- 2 b$ .

$\frac{- (2 b) - 3}{b + 5} = 0$

Step 2.7

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- (2 b) - 1 (3)}{b + 5} = 0$

Step 2.8

Factor $- 1$ out of $- (2 b) - 1 (3)$ .

$\frac{- (2 b + 3)}{b + 5} = 0$

Step 2.9

Rewrite $- (2 b + 3)$ as $- 1 (2 b + 3)$ .

$\frac{- 1 (2 b + 3)}{b + 5} = 0$

Step 2.10

Move the negative in front of the fraction.

$- \frac{2 b + 3}{b + 5} = 0$

Step 3

Set the numerator equal to zero.

$2 b + 3 = 0$

Step 4

Solve the equation for $b$ .

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Step 4.1

Subtract $3$ from both sides of the equation.

$2 b = - 3$

Step 4.2

Divide each term in $2 b = - 3$ by $2$ and simplify.

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Step 4.2.1

Divide each term in $2 b = - 3$ by $2$ .

$\frac{2 b}{2} = \frac{- 3}{2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 b}{2} = \frac{- 3}{2}$

Step 4.2.2.1.2

Divide $b$ by $1$ .

$b = \frac{- 3}{2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$b = - \frac{3}{2}$