If |x - 3/4|

Question

If  |x - \frac{3}{4}| < \frac{9}{4} , which of the following could be a value of x?

A. -3
B. -2
C. 2
D. 3
E. 6

eakabuah · Answer

We are to find possible values of x that satisfy |x-3/4|<9/4
|x-3/4|<9/4 can be rewritten as -9/4<(x-3/4)<9/4
-9/4+3/4<x<9/4+3/4
-3/2<x<3
This means that x>-3/2 and x<3.

From the answer options only option C, x=2 satisfy this condition.
The answer is therefore C.

Posted from my mobile device

Mohammadmo · Answer

X- 3/4<9/4 ==》x<12/4 
-X+3/4< 9/4==》x>-6/4
Just option C can be in the range of x; -1.5<x<3

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firas92 · Answer

\frac{-9}{4}<x-\frac{3}{4}<\frac{9}{4}

\frac{-6}{4}<x<\frac{12}{4}

-1.5<x<3

Out of all the answer choices, only 2 is within this range

Answer is  (C)

CrackverbalGMAT · Answer

In a question like this on Absolute values, instead of using the definition of |x-a|, using the distance approach will help you solve the question much faster.
Remember that |x-a| is the distance of the number x from the number a, on the number line.

So, essentially, this question is telling us that the distance of x from ¾ should be less than 9/4.
Let’s plot a number line and identify the critical points:

Attachment:

13th Aug 2019 - Reply 4.JPG [ 16.99 KiB | Viewed 6291 times ]

The 3 critical points in this situation are:

¾

¾ + \(\frac{9}{4}\) = 3

¾ - \(\frac{9}{4}\) = - 1.5

When we plot these points on the number line, it’s easy to figure out that x has to be between -1.5 and 3 if its distance from ¾ has to be less than \(\frac{9}{4}\).

From this, options A, B and E can be eliminated quite easily. However, option D can be eliminated because of the fact that the distance has to be LESS THAN \(\frac{9}{4}\) and not equal to \(\frac{9}{4}\); hence, x cannot be equal to 3, it has to be LESS THAN 3.

The correct answer option, therefore, is C.

Hope this helps!

Bunuel · Answer

Video Explanation

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bumpbot · Answer

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If |x - 3/4| < 9/4, which of the following could be a value of x?

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