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10 Nov 2023, 08:20
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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64% (01:41) correct
36%
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wrong
based on 519
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How many values of x satisfy the equation ||x - 7| - 9| = 11?
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
12 Nov 2023, 03:27
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Bunuel
OA is B
Posted from my mobile device
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14 Oct 2024, 08:06
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We need to find how many values of x satisfy the equation ||x - 7| - 9| = 11?
Now, | |x - 7| - 9 | = 11
=> |x - 7| - 9 = 11 or -11
=> |x - 7| = 20 or -2
But modulus of a number cannot be negative
=> |x - 7| = 20
So, there are two solutions for x = -13, 20
So, Answer will be B
Hope it helps!
Watch the following video to MASTER Absolute Values
Now, | |x - 7| - 9 | = 11
=> |x - 7| - 9 = 11 or -11
=> |x - 7| = 20 or -2
But modulus of a number cannot be negative
=> |x - 7| = 20
| We have two cases as we have |x - 7| | |
| -Case 1: x - 7 ≥ 0 or x ≥ 7 => | x - 7 | = x - 7 => x - 7 = 20 => x = 27 But the condition was x ≥ 7 and 20 ≥ 7 => x = 20 is a SOLUTION | -Case 2: x - 7 ≤ 0 or x ≤ 7 => | x - 7 | = -(x - 7) = 7 - x => 7 - x = 20 => x = -13 The condition was x ≤ 7 and -13 ≤ 7 => x = -13 is a SOLUTION |
So, there are two solutions for x = -13, 20
So, Answer will be B
Hope it helps!
Watch the following video to MASTER Absolute Values
19 Mar 2026, 09:15
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Deconstructing the Question
We are given: \(||x - 7| - 9| = 11\)
Key idea: If \(|A| = 11\), then
\(A = 11\) or \(A = -11\)
Here \(A = |x - 7| - 9\)
Case 1:
\(|x - 7| - 9 = 11\)
\(|x - 7| = 20\)
\(x - 7 = 20\) → \(x = 27\)
\(x - 7 = -20\) → \(x = -13\)
Case 2:
\(|x - 7| - 9 = -11\)
\(|x - 7| = -2\)
No solution since absolute value cannot be negative
Answer D
We are given: \(||x - 7| - 9| = 11\)
Key idea: If \(|A| = 11\), then
\(A = 11\) or \(A = -11\)
Here \(A = |x - 7| - 9\)
Case 1:
\(|x - 7| - 9 = 11\)
\(|x - 7| = 20\)
\(x - 7 = 20\) → \(x = 27\)
\(x - 7 = -20\) → \(x = -13\)
Case 2:
\(|x - 7| - 9 = -11\)
\(|x - 7| = -2\)
No solution since absolute value cannot be negative
Answer D
