Algebra Examples

$\frac{x + 2}{3 x + 8} = \frac{3}{8}$

Step 1

Subtract $\frac{3}{8}$ from both sides of the equation.

$\frac{x + 2}{3 x + 8} - \frac{3}{8} = 0$

Step 2

Simplify $\frac{x + 2}{3 x + 8} - \frac{3}{8}$ .

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Step 2.1

To write $\frac{x + 2}{3 x + 8}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{x + 2}{3 x + 8} \cdot \frac{8}{8} - \frac{3}{8} = 0$

Step 2.2

To write $- \frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{3 x + 8}{3 x + 8}$ .

$\frac{x + 2}{3 x + 8} \cdot \frac{8}{8} - \frac{3}{8} \cdot \frac{3 x + 8}{3 x + 8} = 0$

Step 2.3

Write each expression with a common denominator of $(3 x + 8) \cdot 8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{x + 2}{3 x + 8}$ by $\frac{8}{8}$ .

$\frac{(x + 2) \cdot 8}{(3 x + 8) \cdot 8} - \frac{3}{8} \cdot \frac{3 x + 8}{3 x + 8} = 0$

Step 2.3.2

Multiply $\frac{3}{8}$ by $\frac{3 x + 8}{3 x + 8}$ .

$\frac{(x + 2) \cdot 8}{(3 x + 8) \cdot 8} - \frac{3 (3 x + 8)}{8 (3 x + 8)} = 0$

Step 2.3.3

Reorder the factors of $(3 x + 8) \cdot 8$ .

$\frac{(x + 2) \cdot 8}{8 (3 x + 8)} - \frac{3 (3 x + 8)}{8 (3 x + 8)} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{(x + 2) \cdot 8 - 3 (3 x + 8)}{8 (3 x + 8)} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Apply the distributive property.

$\frac{x \cdot 8 + 2 \cdot 8 - 3 (3 x + 8)}{8 (3 x + 8)} = 0$

Step 2.5.2

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

$\frac{8 \cdot x + 2 \cdot 8 - 3 (3 x + 8)}{8 (3 x + 8)} = 0$

Step 2.5.3

Multiply $2$ by $8$ .

$\frac{8 \cdot x + 16 - 3 (3 x + 8)}{8 (3 x + 8)} = 0$

Step 2.5.4

Apply the distributive property.

$\frac{8 x + 16 - 3 (3 x) - 3 \cdot 8}{8 (3 x + 8)} = 0$

Step 2.5.5

Multiply $3$ by $- 3$ .

$\frac{8 x + 16 - 9 x - 3 \cdot 8}{8 (3 x + 8)} = 0$

Step 2.5.6

Multiply $- 3$ by $8$ .

$\frac{8 x + 16 - 9 x - 24}{8 (3 x + 8)} = 0$

Step 2.5.7

Subtract $9 x$ from $8 x$ .

$\frac{- x + 16 - 24}{8 (3 x + 8)} = 0$

Step 2.5.8

Subtract $24$ from $16$ .

$\frac{- x - 8}{8 (3 x + 8)} = 0$

Step 2.6

Factor $- 1$ out of $- x$ .

$\frac{- (x) - 8}{8 (3 x + 8)} = 0$

Step 2.7

Rewrite $- 8$ as $- 1 (8)$ .

$\frac{- (x) - 1 (8)}{8 (3 x + 8)} = 0$

Step 2.8

Factor $- 1$ out of $- (x) - 1 (8)$ .

$\frac{- (x + 8)}{8 (3 x + 8)} = 0$

Step 2.9

Rewrite $- (x + 8)$ as $- 1 (x + 8)$ .

$\frac{- 1 (x + 8)}{8 (3 x + 8)} = 0$

Step 2.10

Move the negative in front of the fraction.

$- \frac{x + 8}{8 (3 x + 8)} = 0$

Step 3

Set the numerator equal to zero.

$x + 8 = 0$

Step 4

Subtract $8$ from both sides of the equation.

$x = - 8$