Home » Past Questions » Mathematics » Let f(x) = 2x + 4 and g(x) = 6x + 7 here g(x) > 0. Solve the inequality \(\frac{f(x)}{g(x)}\) < 1....

Let f(x) = 2x + 4 and g(x) = 6x + 7 here g(x) > 0. Solve the inequality \(\frac{f(x)}{g(x)}\) < 1....


Question

Let f(x) = 2x + 4 and g(x) = 6x + 7 here g(x) > 0. Solve the inequality \(\frac{f(x)}{g(x)}\) < 1.

Options

A) x < - \(\frac{3}{4}\)

B) x > - \(\frac{4}{3}\)

C) x > - \(\frac{3}{4}\)

D) x > - 12

The correct answer is C.

Explanation:

\(\frac{f(x)}{g(x)}\) < 1

∴ \(\frac{2x +4}{6x + 7}\) < 1

= 2x + 4 < 6x + 7

= 6x + 7 > 2x + 4
= 6x - 2x > 4 - 7
= 4x > -3
∴ x > -\(\frac{3}{4}\)


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