g.shankaran wrote:which of the following inequalities has a solution set that when graphed on the number line, is a single line segment of finite length?

1. x^4 >=1
2. x^3 >= 27
3. x^2 >= 16
4. 2<=|x|<= 5
5. 2 <= 3x+4 <= 6

Can you please explain

You want an inequality that allows values of x along a single finite range: for example, 3<x<10 is such a finite range, since x is limited from both sides - it can't go lower than 3, or higher than 10.

Once you get this, A, B, and C are eaasily eliminated: they all allow an infinite range of x. For x^4>=1, x can be 2, 3, 4, 5, 6, 10,000, a billion, all of which, when rasied to the power of 4, will be greater than 1. there's no upper limit to x. The same goes for B and C.

Eliminating D is slighty trickier, since x is indeed limited on both sides. The problem with D is that the solution set of x (the range of possible values of x) is not a single finite line: x can be either 2<=x<=5 OR -5<=x<=-2 - so there are two lines that represent the possible values for x according to the inequality.

E is the only one where x has a single, limited range of possible values
2 <= 3x+4 <= 6 /-4
-2 <= 3x <= 2 /:3
-2/3 <= x <= 2/3

X has an upper and lower limit (so it's finite), and there's only a single range of values for x. E is the answer.

Thanks for the reply