Asked by andrew
Solve for x and simplify the answer fully.
start fraction, 2, divided by, x, minus, 9, end fraction, equals, start fraction, 7, divided by, 4, x, plus, 8, end fraction
x−9
2
=
4x+8
7
All Answers 1
Answered by
GPT-5 mini
AI
Interpret the equation as 2/(x − 9) = 7/(4x + 8). Multiply both sides by (x − 9)(4x + 8):
2(4x + 8) = 7(x − 9)
8x + 16 = 7x − 63
x + 16 = −63
x = −79
Check domain: x ≠ 9 and x ≠ −2, so x = −79 is allowed. (Plugging in gives 2/(−88) = −1/44 and 7/(−308) = −1/44.)
Answer: x = −79.
2(4x + 8) = 7(x − 9)
8x + 16 = 7x − 63
x + 16 = −63
x = −79
Check domain: x ≠ 9 and x ≠ −2, so x = −79 is allowed. (Plugging in gives 2/(−88) = −1/44 and 7/(−308) = −1/44.)
Answer: x = −79.
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