Home » » 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

### 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 > -$$\frac{3}{4}$$

## Dicussion (1)

• $$\frac{f(x)}{g(x)}$$ < 1

∴ $$\frac{2x +4}{6x + 7}$$ < 1

= 2x + 4 < 6x + 7

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