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Question
Solve the following inequalities
4n + 7 ≥ 3n + 10, n is an integer
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Solution
4n + 7 ≥ 3n + 10
Subtracting 3n on both sides
4n + 7 – 3n ≥ 3n + 10 – 3n
n(4 – 3) + 7 ≥ 3n + 10 – 3n
n(4 – 3) + 7 ≥ n(3 – 3) + 10
n + 7 ≥ 10
Subtracting 7 on both sides
n + 7 – 7 ≥ 10 – 7
n ≥ 3
Since the solution is an integer and is greater than or equal to 3, the solution will be 3, 4, 5, 6, 7, …..
n = 3, 4, 5, 6, 7, ….
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