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Solve 22 < \frac{m + 7}{4} < 32 Show all your working. - Edexcel - GCSE Maths - Question 20 - 2018 - Paper 2

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Solve-22-<-\frac{m-+-7}{4}-<-32--Show-all-your-working.-Edexcel-GCSE Maths-Question 20-2018-Paper 2.png

Solve 22 < \frac{m + 7}{4} < 32 Show all your working.

Worked Solution & Example Answer:Solve 22 < \frac{m + 7}{4} < 32 Show all your working. - Edexcel - GCSE Maths - Question 20 - 2018 - Paper 2

Step 1

22 < \frac{m + 7}{4}

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Answer

To solve the first part, we start by isolating (m):

  1. Multiply all terms by 4 to eliminate the fraction: 22×4<m+722 \times 4 < m + 7 88<m+788 < m + 7

  2. Subtract 7 from both sides: 88−7<m88 - 7 < m 81<m81 < m This simplifies to: m>81m > 81

Step 2

\frac{m + 7}{4} < 32

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Answer

Next, we solve the second part:

  1. Again, multiply all terms by 4: m+7<32×4m + 7 < 32 \times 4 m+7<128m + 7 < 128

  2. Subtract 7 from both sides: m<128−7m < 128 - 7 m<121m < 121

Step 3

Combine the results

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Answer

Now we combine the results from both inequalities: 81<m<12181 < m < 121

Thus, the final solution is: m∈(81,121)m \in (81, 121)

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