Question

Solve for x and simplify the answer fully.
start fraction, 4, x, minus, 3, divided by, 2, x, minus, 7, end fraction, equals, start fraction, 5, divided by, 3, end fraction
2x−7
4x−3
​
=
3
5

Answer 1

Solve (4x − 3)/(2x − 7) = 5/3.

Cross-multiply: 3(4x − 3) = 5(2x − 7)
=> 12x − 9 = 10x − 35
=> 2x = −26
=> x = −13.

Check denominator: 2x − 7 ≠ 0 ⇒ x ≠ 7/2, so x = −13 is valid.

Answer: x = −13.