Solve 11 < 4x + 1 ≤ 21 ; x ∈ z
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Answer:
The possible values that x can take to satisfy the given the inequality are 3, 4, 5
Step-by-step explanation:
Given that 11 < 4x + 1 ≤ 21 ; x ∈ Z
Subtracting 1 from each inequality, we get
11-1 < 4x + 1-1 ≤ 21-1 ; x ∈ Z
=> 10 < 4x ≤ 20
As 2 is common in all the terms, we can simplify it.
=> 5 < 2x ≤ 10
We need to find x. Therefore, dividing by 2
=> 5/2 < x ≤ 5
=> 2.5 < x ≤ 5
Therefore, x can take up values 2.5 and 5 (5 included) to satisfy the given the inequality.
But it is given that x ∈ Z
Therefore, the possible values that x can take to satisfy the given the inequality are 3, 4, 5
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