Question

Solve the equation and verify your answer:

(9x-7)/(3x+5) = (3x-4)/(x+6)

Answer 1

We have,

(9x-7)/(3x+5) = (3x-4)/(x+6)

(9x-7)/(3x+5) – (3x-4)/(x+6) = 0

By taking LCM as (3x+5) (x+6)

((9x-7) (x+6) – (3x-4) (3x+5)) / (3x+5) (x+6) = 0

By cross-multiplying we get,

(9x-7) (x+6) – (3x-4) (3x+5) = 0

Upon expansion we get,

9x² + 54x – 7x – 42 – (9x² + 15x – 12x – 20) = 0

44x – 22 = 0

44x = 22

x = 22/44

= 2/4

= 1/2

Now let us verify the given equation,

(9x-7)/(3x+5) = (3x-4)/(x+6)

By substituting the value of ‘x’ we get,

(9(1/2) – 7) / (3(1/2) + 5) = (3(1/2) – 4) / ((1/2) + 6)

(9/2 – 7) / (3/2 + 5) = (3/2 – 4) / (1/2 + 6)

((9-14)/2) / ((3+10)/2) = ((3-8)/2) / ((1+12)/2)

-5/2 / 13/2 = -5/2 / 13/2

-5/13 = -5/13

Hence, the given equation is verified.