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Question
The number of integral solutions of the linear inequality 1 ≤ |x –2 | ≤ 3 is
The number of integral solutions of the linear inequality 1 ≤ |x –2 | ≤ 3 is
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Solution
The correct option is C 6
Given that 1 ≤ |x –2 | ≤ 3.
⇒ |x −2| ≥ 1 and |x −2| ≤ 3
⇒ (x – 2 ≤ – 1 or x – 2 ≥ 1) and (– 3 ≤ x – 2 ≤ 3)
⇒ (x ≤ 1 or x ≥ 3) and (– 1 ≤ x ≤ 5)
⇒ x ∈ (– ∞, 1] ∪ [3, ∞) and x ∈ [ –1, 5]
Combining the solutions of two inequalities,we have
x ∈ [–1, 1] ∪ [3, 5]
The integral values of x satisfying given linear inequality are
x = -1, 0, 1, 3, 4, 5.
Number of integral values of x = 6.
Given that 1 ≤ |x –2 | ≤ 3.
⇒ |x −2| ≥ 1 and |x −2| ≤ 3
⇒ (x – 2 ≤ – 1 or x – 2 ≥ 1) and (– 3 ≤ x – 2 ≤ 3)
⇒ (x ≤ 1 or x ≥ 3) and (– 1 ≤ x ≤ 5)
⇒ x ∈ (– ∞, 1] ∪ [3, ∞) and x ∈ [ –1, 5]
Combining the solutions of two inequalities,we have
x ∈ [–1, 1] ∪ [3, 5]
The integral values of x satisfying given linear inequality are
x = -1, 0, 1, 3, 4, 5.
Number of integral values of x = 6.
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