Question

Solve the inequality: 3x−2>−5,

7x+4<−17
and
x>−3
or
x<−1

A. x<−1
B. −3C. x>1
D. −1

Answer 1

The solution to the inequality 3x-2>-5, 7x+4<-17, and x>-3 or x<-1 is nonexistent as no number can satisfy all conditions simultaneously; x cannot be both greater than -1 and less than -3.

Step-by-step explanation:

The student asked to solve the inequality comprised of three parts: 3x-2>-5, 7x+4<-17, and a combination of x>-3 or x<-1. Let's solve each part separately:

1. 3x - 2 > -5
   Add 2 to both sides: 3x > -3
   Divide both sides by 3: x > -1
2. 7x + 4 < -17
   Subtract 4 from both sides: 7x < -21
   Divide both sides by 7: x < -3
3. The third part is already given as x > -3 or x < -1

When we combine all three inequalities, we find that x must satisfy all conditions simultaneously:
The solution is the intersection of x > -1 and x < -3, which is impossible, as there's no number that is both greater than -1 and smaller than -3 at the same time. Therefore, there is no solution to the inequality as given.
In the context of the given multiple choice answers, none of the options are correct since none of them can satisfy the combined inequalities.