Question

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

Answer 1

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.

`3/(x - 7) = 2/(4x + 1)`
`3(4x + 1) = 2(x - 7)`
`12x + 3 = 2x - 14`
`12x - 2x + 3 = 2x - 2x - 14`
`10x + 3 = -14`
`10x + 3 - 3 = -14 - 3`
`10x = -17`
`10x/10 = -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)
`3/-8.7 = 2/-5.8`
`-0.3448275862 = -0.3448275862`

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