Question

An inequality is shown. 12+11/6x≤ 5+3x Select the statement(s) and number line(s) that can represent the inequality. Click all that apply. a. The solution set is {6, [infinity]} for x ∈ R. b. The solution set is {6, 7, 8, …} for x ∈ N. c. 6 ≤ x d. The value of a number substituted for x is greater than 6. (more options below.)

Answer 1

(a)The solution set is:
`x \in [6, \infty) \forall x \in R`

(c)
`6 \leq x`

Explanation:

Given the inequality:
`12+(11)/(6)x\leq 5+3x`

We solve by collecting like terms

`12+(11)/(6)x\leq 5+3x\\12-5\leq 3x-(11)/(6)x\\7\leq (18x-11x)/(6)\\42 \leq 7x\\$Divide both sides by 7\\6 \leq x\\$We can re-write this as:\\x\geq 6`

The solution set is therefore:
`x \in [6, \infty) \forall x \in R`