Make p the subject of the relation: q = $\frac{3p}{r} + \frac{s}{2}$

Analyze the question: We need to isolate p in q = 3p/r + s/2.

Concept: Use inverse operations. First move the term without p to the other side, then clear the fractions, then divide by the coefficient of p.

Solution:

1. Start with: q = 3p/r + s/2

2. Subtract s/2 from both sides: q − s/2 = 3p/r

3. Combine the left side over a common denominator: (2q − s)/2 = 3p/r

4. Cross-multiply: r(2q − s) = 6p

5. Divide by 6: p = r(2q − s)/6 = (2qr − rs)/6

Check against the options:

• A: (2q − rs)/6 is wrong because r was not multiplied through the q term.
• B: wrong form entirely.
• C: (2qr − s)/6 is wrong because r was not multiplied through the s term.
• D: (2qr − rs)/6 matches our result.

Tip: When you clear fractions, multiply every term by the denominator. Here r multiplies both 2q and s. A quick check is to substitute simple numbers, such as p = 2, r = 1, s = 2. Then q = 6 + 1 = 7, and option D gives (14 − 2)/6 = 2, which is correct.