Inequalities

[carllecat]

Which of the following inequalities has a solution that, when graphed on the number line, is a single line segment of a finite length?

A) x^4 >= 1
B) x^3 <= 27
C) x^2 >= 16
D) 2 <= |x| <= 5
E) 2 <= 3X+4 <= 6

Answer to be posted later.

[carllecat]

E) 2 <= 3x+4 <= 6

[carllecat]

As dumb as it might seem, I can't get the wright answer.

[mp2437]

Choice E is the only choice of a linear function, or in other terms, a straight line.
Choices A-C are 4,3, and 2 degree polynomial equations, respectively, so there lines will be curved.
Choice D is an absolute value, so you could have y = 2,3,4,5 when x > 0, or you could have y = -2,-3,-4,-5 when x < 0, so the graph looks like this:

https://www.maths.abdn.ac.uk/~igc/tch/ma ... ode14.html

Clearly, you can see that it is not a single line segment.

Choice E says that 2 <=3x+4 <=6, or doing the algebra, -2/3 < = x <= 2/3, so you know that this choice is a line with a defined length (anywhere from -2/3 up to 2/3), and is a straight line.