Inequality

[moonlite]

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

a) x^4 >= 1
b) x^3 <= 27
c) x^2 >= 16
d) 2<= |x| <=5
e) 2<= 3x + 4 <= 6

I easily eliminated a b and c, can someone please help me with d and e.

Thanks

OA E

[4seasoncentre]

If you imagine the number line for D.

You would have a solid dot at 2 connecting to a solid dot at 5.

All the values from 2 to 5 inclusive are valid for that statement.

HOWEVER, if X = -2
then, |x| = 2

so -2 is a valid value of X for the statement, as are all of the values from -5 to -2

So we would have 2 finite line segments on the number line.

[VP_Jim]

For (D), x could be anywhere between positive 2 and positive 5, OR it could be anywhere between -2 and -5. In either case, its absolute value is between 2 and 5. Thus, it is not a single line segment.

Solving for "x" in (E) shows that it must be between -2/3 and 2/3. Thus, it is finite and a single segment. Try plugging in some values just to make sure.

Good question!

[moonlite]

Thanks guys!