Make x the subject of the equation s = 2 + $\frac{t}{5}$(x + ⅗y)

Analyze the question: We need to rearrange s = 2 + (t/5)(x + 3y/5) so that x stands alone on one side.

Concept: Undo the operations in reverse order: subtract the constant, remove the fraction multiplying the bracket, then subtract the term that sits with x.

Solution:

1. Start with: s = 2 + (t/5)(x + 3y/5)

2. Subtract 2 from both sides: s − 2 = (t/5)(x + 3y/5)

3. Multiply both sides by 5/t, which removes the factor t/5: 5(s − 2)/t = x + 3y/5

4. Subtract 3y/5 from both sides: x = 5(s − 2)/t − 3y/5

Checking the options:

• A. x = 5[(s − 2) ÷ t] − 3/5 y. This is 5(s − 2)/t − 3y/5, which matches our result exactly.
• B. Has 25 and 3ty, which do not appear in our working.
• C and D. Have an incorrect structure and do not match.

Note on reading the question: The term "⅗y" means (3/5)·y. Option A's "3/5y" is read as (3/5)y, which is the same thing.

Exam tip: For "make x the subject" questions, work backwards. Move the terms that are furthest from x first (here the +2, then the multiplier t/5, then 3y/5). Always do the same operation to both sides, and check by substituting simple values if time allows.