Which of the following inequalities...

Question

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

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

I came across this question when taking a CAT, it was apparent that a,b and c were not the right answer, but I had a hard time deciding between d and e.

gurpreetsingh · Answer

Its clearly E. Just plug values for d -3, 3 satisfies but -1 does not. And -1 comes between -3 and 3 => Its not a single line segment. But the best way is to use algebra. take cases |x| <=5 => -5<= x <= 5 |x| >=2 => -2 >= x >= 2 . Now just draw it,its not single line segment.

krishna3891 · Answer

e should be the answer as the slope lies within finite boundaries. The solution for d is -infinity to -2 and 5 to infinity

cipher · Answer

Its E , you can use POE in this one, you don't even have to calculate to get the answer. Options 1,2 and 3 are clearly out.

Between D and E if you see the equation in D it's |x| which means X has 2 values +X and -X and hence it will form 2 equations 2<= -x <= 5 and 2<= +x <= 5 which means it will form 2 lines .. !

I hope this help .!

perseverant · Answer

Thank you all! it has now become obvious why the answer is E.

hardnstrong · Answer

I could not understand the question .......can anyone explain in more details
Thanks

perseverant · Answer

Basically the question is asking which inequality when graphed is a line with a defined start and end point. Options a,b, and c are inmediately out because you only have one point and you dont know where the line ends, so it would be a infinite line and not finite like the question is asking.
Option D, would give 2 lines because of the absolute value, because x could be positive or negative.
Then the only option left is d which gives a defined range for x (start and end point), which is a one finite line.

perseverant · Answer

Correction I meant the only option left is E.

hardnstrong · Answer

this is the confusing part for me

1st option says x^4=1
(so x can be 1 or -1) 2 points

same is the case with option 3

perseverant · Answer

for the 1st option, the key is that x can be 1 OR -1, not AND which would give you 2 infinite lines because in both cases you have a start points, not end points. The same happens with option 3.

hardnstrong · Answer

Got it now .....THANKS

seekmba · Answer

For option E, i got e) 2 <= 3x+4 <=6 -2/3 <= x <= -2 and -10/3 <= x <= 2/3 How do the above equations suggest that it is a finite line. I am sorry but I still dont understand....

Which of the following inequalities...

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