Question

Solve the equation. Check for extraneous solutions. 2[7-7x]=2x+4
A. x =3/2 or x = 5/6
B. x =3/2 or x =5/8
C. x = 5/8
D. x = 3/2

Answer 1

To solve this problem you must apply the proccedure shown below:

1. You have the following expression:

$2[7-7x]=2x+4$

2. To solve it, you must solve for the variable $x$, as following:

$14-14x=2x+4 \\ x= \frac{10}{16} \\ x= \frac{5}{8}$

3. Checking for extraneous solutions:

$x= \frac{5}{8} \\ 2[7-7( \frac{5}{8}) ]=2 (\frac{5}{8}) +4 \\ \frac{21}{4} = \frac{21}{4}$

$\frac{5}{8}$ is a solution.

The answer is the option C: $x=\frac{5}{8}$