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16 Sep 2014, 00:41
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How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?
A. 2
B. 3
C. 4
D. 5
E. 6
A. 2
B. 3
C. 4
D. 5
E. 6
16 Sep 2014, 00:41
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Official Solution:
How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?
A. 2
B. 3
C. 4
D. 5
E. 6
\(|x-3.5| \lt 2\) means that \(-2 \lt x-3.5 \lt 2\).
Now, add 3.5 to all three parts: \(1.5 \lt x \lt 5.5\).
Since given that \(x\) is an integer, then it can take the following four values: 2, 3, 4, and 5.
Answer: C
How many integers \(x\) are there so that \(|x - 3.5| \lt 2\)?
A. 2
B. 3
C. 4
D. 5
E. 6
\(|x-3.5| \lt 2\) means that \(-2 \lt x-3.5 \lt 2\).
Now, add 3.5 to all three parts: \(1.5 \lt x \lt 5.5\).
Since given that \(x\) is an integer, then it can take the following four values: 2, 3, 4, and 5.
Answer: C
18 Apr 2016, 07:53
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Using the number line approach :
Ex.
|X - A| < N
"A" represents the center or origin of imaginary line. "N" represents the absolute value of length on both sides of our new center (A).
Line should look like - |---------------(A-N)------A------(A+N)---------------|. "X" represents the range highlighted.
For the given problem: A = 3.5 & N = 2. Applying above logic, range (X) should look like : 1.5 < X < 5.5
Clearly, there are 4 integers (2, 3, 4, 5) within the given range.
Cheers.
Ex.
|X - A| < N
"A" represents the center or origin of imaginary line. "N" represents the absolute value of length on both sides of our new center (A).
Line should look like - |---------------(A-N)------A------(A+N)---------------|. "X" represents the range highlighted.
For the given problem: A = 3.5 & N = 2. Applying above logic, range (X) should look like : 1.5 < X < 5.5
Clearly, there are 4 integers (2, 3, 4, 5) within the given range.
Cheers.
