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.)

(a)The solution set is:

(c)

Step-by-step explanation:

Given the inequality:

We solve by collecting like terms

The solution set is therefore:

12

step-by-step explanation:

12 + 5 = 17

12x2=24

24-7=17

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.