# How do you solve 3/(x-7)=2/(4x+1) and check for extraneous solutions?

Oct 19, 2016

The solution of the equation is $x = - 1.7$, and it is not extraneous.

#### Explanation:

To solve this proportion, begin by cross multiplying. This will give you an equation in familiar form.

$\frac{3}{x - 7} = \frac{2}{4 x + 1}$
$3 \left(4 x + 1\right) = 2 \left(x - 7\right)$
$12 x + 3 = 2 x - 14$
$12 x - 2 x + 3 = 2 x - 2 x - 14$
$10 x + 3 = - 14$
$10 x + 3 - 3 = - 14 - 3$
$10 x = - 17$
$10 \frac{x}{10} = - \frac{17}{10}$
$x = - 1.7$

To check whether the solution is extraneous, substitute $- 1.7$ for $x$ in the original equation to see whether the two sides of the equation are equal. If they are, the answer is a solution. If they are not, the answer is an extraneous solution.

3/(-1.7 - 7) = 2/(4*-1.7 + 1) 3/-8.7 = 2/(-6.8 + 1)
$\frac{3}{-} 8.7 = \frac{2}{-} 5.8$
$- 0.3448275862 = - 0.3448275862$

Since the equation is true, $- 1.7$ is a solution.