n is an integer such that $3n + 2 \\leq 14$ and $\frac{6n}{n + 5} > 1$\nFind all the possible values of n. - Edexcel - GCSE Maths - Question 20 - 2018 - Paper 1
Question 20
n is an integer such that $3n + 2 \\leq 14$ and $\frac{6n}{n + 5} > 1$\nFind all the possible values of n.
Worked Solution & Example Answer:n is an integer such that $3n + 2 \\leq 14$ and $\frac{6n}{n + 5} > 1$\nFind all the possible values of n. - Edexcel - GCSE Maths - Question 20 - 2018 - Paper 1
Step 1
$3n + 2 \\leq 14$
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Answer
To solve the inequality, we start by isolating n.\nSubtract 2 from both sides:\n\n3nleq12\n\nThen, divide by 3:\n\nnleq4\n\nThis gives us our first limitation on n: it must be less than or equal to 4.
Step 2
$\frac{6n}{n + 5} > 1$
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Answer
Next, we will solve the second inequality. To eliminate the fraction, multiply both sides by (n+5) (noting that n+5>0 for positive values of n):\n\n6n>n+5\n\nRearranging gives us:\n\n6n−n>5\n\nWhich simplifies to:\n\n5n>5\n\nDividing both sides by 5, we find:\n\nn>1\n\nNow we have a second limitation: n must be greater than 1.
Step 3
Combining inequalities
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Answer
We now combine our two findings:\n\n1. nleq4\n2. n>1\n\nThe solution is that n must be an integer satisfying both conditions. Thus, the possible integer values for n are: 2,3,4.
