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n is an integer such that $3n + 2 \\leq 14$ and $\frac{6n}{n + 5} > 1$ Find all the possible values of n. - Edexcel - GCSE Maths - Question 20 - 2018 - Paper 1

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n-is-an-integer-such-that-$3n-+-2-\\leq-14$-and-$\frac{6n}{n-+-5}->-1$--Find-all-the-possible-values-of-n.-Edexcel-GCSE Maths-Question 20-2018-Paper 1.png

n is an integer such that $3n + 2 \\leq 14$ and $\frac{6n}{n + 5} > 1$ Find all the possible values of n.

Worked Solution & Example Answer:n is an integer such that $3n + 2 \\leq 14$ and $\frac{6n}{n + 5} > 1$ Find all the possible values of n. - Edexcel - GCSE Maths - Question 20 - 2018 - Paper 1

Step 1

Solve the inequality $3n + 2 \leq 14$

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Answer

To solve for n, start with the inequality:

3n+2≤143n + 2 \leq 14

Subtract 2 from both sides:

3n≤123n \leq 12

Now, divide both sides by 3:

n≤4n \leq 4

This gives us the upper bound for n.

Step 2

Solve the inequality $\frac{6n}{n + 5} > 1$

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Answer

Next, we solve the second inequality:

6nn+5>1\frac{6n}{n + 5} > 1

Cross-multiplying gives:

6n>n+56n > n + 5

Subtract n from both sides:

5n>55n > 5

Now, divide by 5:

n>1n > 1

This gives us the lower bound for n.

Step 3

Combine the results

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Answer

From both inequalities, we have:

1<n≤41 < n \leq 4

Since n must be an integer, the possible values for n are:

{2,3,4}\{2, 3, 4\}

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