Which of the following inequalities...

[A4Fever]

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

A) X6 ≥1
B) X5≤ 27
C) X4≥ 16
D) 4≤ x ≤ 9
E) 3 ≤ 2x+6≤8

Source: GMAC practice test - note that I have changed the numbers to adhere to copywright restrictions.

Question: I hesitated between answers D & E because I would have thought that they both allow you to draw a line segment of finite lenght but I guess I'm missing something. I checked all OG inequalities problems in both guides and did not find a similar problem.

Can anyone please help!?

Thanks
A4Fever

[JonathanSchneider]

Are you sure you copied this correctly? D and E are both correct here, to my reckoning.

[A4Fever]

Yes - I just changed the numbers but did not change the signs (equal or greater than) That's what I figured as well and since GMAC do not provide an explanation, hard for me to figure out. I can post the exact question as a screenshot if it's possible.

[A4Fever]

ohhh my bad - I just noticed that in answer choice D, |x| was between 4 & 9. Given that, I still don't get it ;-)

[esledge]

ohhh my bad - I just noticed that in answer choice D, |x| was between 4 & 9. Given that, I still don't get it ;-)

That would do it. To deal with the absolute value, you must set up two cases for what's inside: positive and negative.

What if x is positive? In that case, |x| = x and you can just drop the bars to get 4 ≤ x ≤ 9.

What if x is negative? In that case, |x| = -x (for example, |-5| = -(-5) = 5). We can eliminate the bars by substituting -x in the inequality, and get 4 ≤ -x ≤ 9. Remember, x is negative, so -x is positive, so it "makes sense" that it can be between 4 and 9. Divide the inequality by -1, remembering to flip the signs: -4 ≥ x ≥ -9.

Put it all together, and we have two finite segments on the number line: -9 ≤ x ≤ -4 and 4 ≤ x ≤ 9. As a check, take any number in those ranges, and its absolute value will be between 4 and 9.