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ExpertsGlobal5
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If |2x 10| < x + 1, which of the following cannot be a value of x? 21 Nov 2025, 22:20
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D
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45% (medium)

Question Stats:

61% (01:17) correct 39% (01:24) wrong based on 398 sessions

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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
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D
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MaitriD
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If |2x 10| < x + 1, which of the following cannot be a value of x? 22 Nov 2025, 04:26
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|2x - 10| < x + 1
2x - 10 < x + 1
x < 11

-2x + 10 < x + 1
9 < 3x
3<x

so, 3 < x < 11

Cannot be I and III
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If |2x 10| < x + 1, which of the following cannot be a value of x? 22 Nov 2025, 05:35
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-x-1<2x-10<x+1

Add 10:
-x+9<2x<x+11

Subtract x:
-2x+9<x<11

From this we get 2 equations:
-2x+9<x and x<11
On solving:
9<3x -> x>3

Hence 3<x<11

0 and 22 not possible values of x.
Ans is D.
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If |2x 10| < x + 1, which of the following cannot be a value of x? 24 Nov 2025, 10:14
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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
Show more


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
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If |2x 10| < x + 1, which of the following cannot be a value of x? 25 Nov 2025, 03:35
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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
Show more
If |2x – 10| < x + 1, then we need to find the values that x cannot take .

removing the Modulus

-(x+1) < (2x-10) < (x+1)

Case 1:

-(x+1) < (2x-10)

-x -1 < 2x - 10

10-1 < 2x + x

9 < 3x

3< x

That’s, x >3

Case 2:

(2x-10) < (x+1)

2x - x < 10+1

x < 11

Thus, the limits are x >3 and x <11 .

The possible values of x are : 4,5,6,7,8,9,10.

The values x cannot take are : 0 and 22.

Option D

D. I and III only
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If |2x 10| < x + 1, which of the following cannot be a value of x? 21 Jan 2026, 02:30
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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
Show more
Experts' Global Video Explanation:

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