n is an integer such that 3n + 2 ≤ 14 and \( \frac{6n}{n + 5} > 1 \)
Find all the possible values of n. - Edexcel - GCSE Maths - Question 1 - 2018 - Paper 2
Question 1
n is an integer such that 3n + 2 ≤ 14 and \( \frac{6n}{n + 5} > 1 \)
Find all the possible values of n.
Worked Solution & Example Answer:n is an integer such that 3n + 2 ≤ 14 and \( \frac{6n}{n + 5} > 1 \)
Find all the possible values of n. - Edexcel - GCSE Maths - Question 1 - 2018 - Paper 2
Step 1
Solve the inequality 3n + 2 ≤ 14
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Answer
To solve this inequality, we first isolate n:
Subtract 2 from both sides:
[ 3n \leq 12 ]
Then divide by 3:
[ n \leq 4 ]
So, the possible values of n from this inequality are all integers less than or equal to 4.
Step 2
Solve the inequality \( \frac{6n}{n + 5} > 1 \)
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Answer
To solve ( \frac{6n}{n + 5} > 1 ):
First, rearrange the inequality:
[ 6n > n + 5 ]
Subtract n from both sides:
[ 5n > 5 ]
Now divide by 5:
[ n > 1 ]
Thus, the possible values of n from this inequality are integers greater than 1.
Step 3
Combine the solutions of both inequalities
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Answer
Now, we combine the results:
From the first inequality, ( n \leq 4 )
From the second inequality, ( n > 1 )
The integer solutions that satisfy both inequalities are: ( n = 2, 3, 4 ).
