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If 3(5x - 7) - 4(8x - 13) = 2 (9x - 11) - 17, then the value of \(\frac{7x -5}{11x-9}\) is
1. \(\frac{9}{13}\)
2. \(\frac{14}{31}\)
3. \(-\frac{14}{31}\)
4. \(-\frac{14}{13}\)

1 Answer

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Correct Answer - Option 1 : \(\frac{9}{13}\)

3(5x - 7) - 4(8x - 13) = 2 (9x - 11) - 17

Calculations:

3(5x - 7) - 4(8x - 13) = 2 (9x - 11) - 17

⇒ 15x - 21 - 32x + 52 = 18x - 22 - 17

⇒ -17x + 31 = 18x - 39

⇒ 18x + 17x = 31 + 39

⇒ 35x = 70

⇒ x = 70/35

⇒ x = 2

\(\frac{7x -5}{11x-9}\) = \(\frac{{7×2 -5}}{{11× 2}-9}\)

⇒ (14 - 5) ÷ (22 - 9)

⇒ 9/13

∴ The required value is 9/13

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