Question

Which inequality is equivalent to

Answer 1

Cross multiply

(x-6)(x+3)=x²-6x+3x+18=x²-3x+18

(x+7)(x+5)=x²+7x+5x+35=x²+12x+35

that means the inequality is

x²-3x+18≥x²+12x+35 which simplifies to

—17≥15x or 15x+17≤0

Answer 2

15x + 53 ≤ 0

Explanation:

The given inequality is
`(x-6)/(x+5)\geq (x+7)/(x+3)`

By cross multiplication

(x - 6)(x + 3) ≥ (x + 5)(x + 7)

x(x + 3) - 6(x + 3) ≥ x(x + 7) + 5(x + 7)

x² + 3x - 6x - 18 ≥ x² + 7x + 5x + 35

x² - 3x - 18 ≥ x² + 12x + 35

- 3x - 18 ≥ 12x + 35

- 18 - 35 ≥ 3x + 12x

15x ≤ -53

15x + 53 ≤ 0

15x + 53 ≤ 0 is the answer.