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Solve 22 < \frac{m + 7}{4} < 32 Show all your working. - Edexcel - GCSE Maths - Question 21 - 2018 - Paper 2

Question 21

$Solve-22-<-\frac{m-+-7}{4}-<-32--Show-all-your-working.-Edexcel-GCSE Maths-Question 21-2018-Paper 2.png$

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 21 - 2018 - Paper 2

Step 1

Step 1: Solve the Left Inequality 22 < \frac{m + 7}{4}

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Answer

To solve the left part of the inequality, we'll first multiply both sides by 4 to eliminate the fraction:

$22 \times 4 < m + 7$

which simplifies to:

$88 < m + 7$

Next, subtract 7 from both sides:

$88 - 7 < m$

Simplifying gives:

$81 < m$

or equivalently:

$m > 81$ .

Step 2

Step 2: Solve the Right Inequality \frac{m + 7}{4} < 32

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Answer

For the right side of the inequality, we again multiply both sides by 4:

$m + 7 < 32 \times 4$

This simplifies to:

$m + 7 < 128$

Now, subtract 7 from both sides:

$m < 128 - 7$

which simplifies to:

$m < 121$ .

Step 3

Step 3: Combine the Results

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Answer

Now we have two inequalities from Steps 1 and 2:

$81 < m < 121.$

The solution set for the inequality is:

$m \in (81, 121).$

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