Given that (3 - y) ÷ 2x = (6y + 7) ÷ (4x - 5), find the value of x when y = 2

Analyze the question: We have an equation in x and y. Substitute y = 2 and solve for x.

Concept: When two fractions are equal, cross-multiply, then collect like terms.

Solution:

The equation is (3 - y)/(2x) = (6y + 7)/(4x - 5).

Substitute y = 2:

• Left side numerator: 3 - 2 = 1
• Right side numerator: 6(2) + 7 = 19

So 1/(2x) = 19/(4x - 5).

Cross-multiply:

1 × (4x - 5) = 19 × 2x

4x - 5 = 38x

-5 = 38x - 4x

-5 = 34x

x = -5/34

Answer: x = -5/34, which is option D.

Check: If x = -5/34, then 2x = -5/17, so the left side is 1 ÷ (-5/17) = -17/5. Also 4x - 5 = -10/17 - 5 = -95/17, so the right side is 19 ÷ (-95/17) = -17/5. Both sides are equal.

Tip: Always substitute the known value first, so the equation becomes simple before cross-multiplying. Watch your signs when moving terms across, because a careless slip could lead you to the wrong option, such as C (5/34).