Question

Which represents the solution set to the inequality 5.1(3 + 2.2x) > –14.25 – 6(1.7x + 4)? x < –2.5 x > 2.5 (–2.5, ∞) (–∞, 2.5)

Answer 1

The inequality simplifies to
  15.3 + 11.22x > -14.25 -10.2x -24
  21.42x > -53.55 . . . . . . . . . . . . . . . . add 10.2x-15.3
  x > -2.5 . . . . . . . . . . . . . . . . . . . . . . . divide by 21.42

The solution set is best represented by
  (-2.5, ∞)

Answer 2

Answer:

The set which represent the solution is (-2.5;+∞).

Step-by-step explanation:

Let's first expands each one of the parenthesis  in the inequality:

5.1(3 + 2.2x) > -14.25 - 6(1.7x + 4)

5.1*3 + 5.1*2.2x > -14.25 - 6*1.7x -6*4

15.3 + 11.22x > -14.25 - 10.2x - 24

Now we must to organize the equition, for dong this we will group the terms which contains the variable x to left member of the inequality and the rest of the term to the right member:

11.22x +10.2x > -14.25  - 24 - 15.3

21.42x >  - 53.55

Solving x:

x >  - 53.55/21.42

x >  - 2.5  

That mean that the solution set is  (-2.5;+∞)