ExpertsGlobal5
If |2x – 10| < x + 1, which of the following cannot be a value of x?
I. 0
II. 7
III. 22
A. I only
B. II only
C. III only
D. I and III only
E. II and III only
Method 1: Solving the Inequality\(|2x - 10| < x + 1\)
For an inequality in the form \(|A| < B\), we set up the compound inequality:
\(-(x + 1) < 2x - 10 < x + 1\)
Split this into two parts:
1.
Left side: \(-x - 1 < 2x - 10\)
\(9 < 3x\)
\(3 < x\)
2.
Right side: \(2x - 10 < x + 1\)
\(x < 11\)
Combining them, we get the valid range: \(3 < x < 11\).
[hr]
Method 2: Evaluating the Question (The Trap)The question asks:
"Which of the following cannot be a value of x?"This means we are looking for values that fall
outside the range \((3, 11)\).
Let's check the statements:
I. \(0\)
Is \(0\) between 3 and 11?
No. So, 0
cannot be a value. (Keep this).
II. \(7\)
Is \(7\) between 3 and 11?
Yes. So, 7
can be a value. (Discard this).
III. \(22\)
Is \(22\) between 3 and 11?
No. So, 22
cannot be a value. (Keep this).
Since statements I and III are the ones that are impossible, the correct option is D.
Answer: D