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How many integers n satisfy the absolute value inequality |4n - 3| <= 2
- a)One
- b)Two
- c)Three
- d)Four
- e)Five
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
How many integers n satisfy the absolute value inequality |4n - 3| <...
To solve the absolute value inequality |4n - 3| ≤ 2, we can consider two cases:
Case 1: 4n - 3 ≥ 0
If 4n - 3 ≥ 0, then |4n - 3| = 4n - 3. In this case, the inequality becomes 4n - 3 ≤ 2, which we can solve as follows:
If 4n - 3 ≥ 0, then |4n - 3| = 4n - 3. In this case, the inequality becomes 4n - 3 ≤ 2, which we can solve as follows:
4n - 3 ≤ 2
4n ≤ 5
n ≤ 5/4
4n ≤ 5
n ≤ 5/4
Case 2: 4n - 3 < 0
If 4n - 3 < 0, then |4n - 3| = -(4n - 3) = -4n + 3. In this case, the inequality becomes -4n + 3 ≤ 2, which we can solve as follows:
If 4n - 3 < 0, then |4n - 3| = -(4n - 3) = -4n + 3. In this case, the inequality becomes -4n + 3 ≤ 2, which we can solve as follows:
-4n + 3 ≤ 2
-4n ≤ -1
n ≥ 1/4
-4n ≤ -1
n ≥ 1/4
Now, we can combine the results from both cases. Since we want to find the integers that satisfy the inequality, we need to find the intersection of the solutions from both cases.
The solutions from Case 1 are n ≤ 5/4, and the solutions from Case 2 are n ≥ 1/4.
The only integer that satisfies both conditions is n = 1.
Therefore, the correct answer is that only one integer, n = 1, satisfies the absolute value inequality.
Hence, the answer is A.
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How many integers n satisfy the absolute value inequality |4n - 3| <= 2a)Oneb)Twoc)Threed)Foure)FiveCorrect answer is option 'A'. Can you explain this answer?
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