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GMAT 1: 640 Q48 V28
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Bunuel
Which of the following could be q if |4q – 5| < 1?

A. –1
B. 1/4
C. 1
D. 5/4
E. 0
You can open brackets the "long" way if you can't remember the compound expression format.*

Case 1: \(4q - 5 < 1\)
\(4q < 6\)
\(q < \frac{6}{4}\)

(Do not reduce this fraction. Two answers have 4 in the denominator.)

Case 2: \(- (4q - 5) < 1\)
Divide by -1 and flip the sign
\(4q - 5 > -1\)
\(4q > 4\)
\(q > 1\)


Write the range:
\(1 < q < \frac{6}{4}\)

Only D fits in the range.
Answer D

I have seen confusion about linear inequality setup. If sign is \(<\) or \(\leq\)? Compound inequality. If sign is \(>\) or \(\geq\)? TWO inequalities. Here is a review.
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Bunuel
Which of the following could be q if |4q – 5| < 1?

A. –1
B. 1/4
C. 1
D. 5/4
E. 0

Looking at our answer choices we can determine that only when q = 5/4 is the given inequality true.

|4(5/4) – 5| < 1

|5 - 5| < 1

0 < 1

Answer: D
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I don't understand this problem sloving at all. Please, Kindly explain it more easily.

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Which of the following could be q if |4q – 5| < 1?
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