Question

Solve for x and simplify the answer fully.
start fraction, 2, x, plus, 2, divided by, x, minus, 8, end fraction, equals, start fraction, 4, divided by, 7, end fraction
x−8
2x+2
​
=
7
4

Answer 1

Solve (2x+2)/(x−8) = 4/7.

Cross-multiply: 7(2x+2) = 4(x−8)
=> 14x + 14 = 4x − 32
=> 10x = −46
=> x = −46/10 = −23/5.

Exclude x = 8 (would make denominator zero). Check: substituting x = −23/5 gives (2x+2)/(x−8) = 4/7.

Answer: x = −23/5.