Question

−18x+21>−15 OR 20x−13≥27minus, 18, x, plus, 21, is greater than, minus, 15, start color #ed5fa6, start text, space, O, R, space, end text, end color #ed5fa6, 20, x, minus, 13, is greater than or equal to, 27 Choose 1 answer: Choose 1 answer:
(Choice A) A x<-2x<−2x, is less than, minus, 2 or x\geq 2x≥2x, is greater than or equal to, 2.
(Choice B) B x=-2x=−2x, equals, minus, 2.
(Choice C) C x\geq 2x≥2x, is greater than or equal to, 2.
(Choice D) D There are no solutions.
(Choice E) E All values of xxx are solutions.

Answer 1

Answer:

E. All values of x are solutions.

Step-by-step explanation:

Given compound inequality,

$-18x+21 > -15\text{ or }20x - 13 \geq 27$

∵ a > b ⇒ a + c > b + c ∀ a, b, c ∈ R,

$-18x > -15 - 21\text{ or }20x \geq 27 + 13$

$-18x > -36\text{ or }20x \geq 40$

∵ a > b ⇒ $\frac{a}{c} > \frac{b}{c}$ if c > 0,

a > b ⇒ $\frac{a}{c} < \frac{b}{c}$ if c < 0,

So,

$x < 2\text{ or } x \geq 2$

$\implies x\in (-\infty, \infty)$

i.e. All values of x are solutions.

OPTION E is correct.