# How do you solve 1 /( 4 x + 2) = 5 and find any extraneous solutions?

Jan 18, 2017

$x = - \frac{9}{20}$

#### Explanation:

Eliminate the fraction on the left side of the equation by multiplying both sides by (4x +2) the denominator of the fraction.

$\Rightarrow \cancel{\left(4 x + 2\right)} \times \frac{1}{\cancel{\left(4 x + 2\right)}} = 5 \left(4 x + 2\right)$

$\Rightarrow 1 = 20 x + 10$

subtract 10 from both sides.

$1 - 10 = 20 x \cancel{+ 10} \cancel{- 10}$

$\Rightarrow 20 x = - 9$

To solve for x, divide both sides by 20

$\frac{\cancel{20} x}{\cancel{20}} = \frac{- 9}{20}$

$\Rightarrow x = - \frac{9}{20} \text{ is the only solution}$