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![How many values of [m]x[/m] are there such that [m]4x[/m] is](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "How many values of [m]x[/m] are there such that [m]4x[/m] is"){kind=icon}
27 Jul 2026, 00:11
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E
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33% (03:06) correct
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How many values of \(x\) are there such that \(4x\) is an integer and \(\displaystyle |x-1|+|x+2|\le 6.5?\)
(A) \(23\)
(B) \(24\)
(C) \(25\)
(D) \(26\)
(E) \(27\)
(A) \(23\)
(B) \(24\)
(C) \(25\)
(D) \(26\)
(E) \(27\)
27 Jul 2026, 03:48
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\(|x+1| ⭢ x+1\) is positive if \(x > -1\)
\(|x+2| ⭢ x+2 \) is positive if \( x<-2\)
Therefore, we have:
(1) \(-x-1-x-2 ≤ \frac{13}{2}\) if \(x ≤ -2\)
(2) \(-x-1+x+2 ≤ \frac{13}{2}\) if \(-2 < x < -1\)
(3) \(x+1+x+2 ≤ \frac{13}{2}\) if \(x ≥ -1\)
By solving the equations, we have:
(1) \(x ≥ -19/4\)
(2) always verified
(3) \(x ≤ 7/4\)
Therefore, the final solution is: \(-19/4 ≤ x ≤ 7/4\).
We need 4x, so we can multiply each side by 4 ⭢ -\(19 ≤ 4x ≤ 7\)
In total we have 27 integers between -19 and 7 (included).
Answer: E
\(|x+2| ⭢ x+2 \) is positive if \( x<-2\)
Therefore, we have:
(1) \(-x-1-x-2 ≤ \frac{13}{2}\) if \(x ≤ -2\)
(2) \(-x-1+x+2 ≤ \frac{13}{2}\) if \(-2 < x < -1\)
(3) \(x+1+x+2 ≤ \frac{13}{2}\) if \(x ≥ -1\)
By solving the equations, we have:
(1) \(x ≥ -19/4\)
(2) always verified
(3) \(x ≤ 7/4\)
Therefore, the final solution is: \(-19/4 ≤ x ≤ 7/4\).
We need 4x, so we can multiply each side by 4 ⭢ -\(19 ≤ 4x ≤ 7\)
In total we have 27 integers between -19 and 7 (included).
Answer: E
29 Jul 2026, 04:09
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