Make x the subject of y = 17/(x + 3): x = (□ − □y)/y Fill in each blank

17, 3. Multiply both sides by x + 3: xy + 3y = 17, xy = 17 − 3y, x = (17 − 3y)/y.

Make x the subject of 7/x + 1 = y: x = □/(y − □) Fill in each blank

7, 1. Take 1 from both sides: 7/x = y − 1; multiply by x, then divide by y − 1: x = 7/(y − 1).

Which is the formula y = 4x + kx − 1 with x as its subject? A. x = (y + 1)/(4k) B. x = (y + 1)/(4 + k) C. x = (y − 1)/(4 + k) D. x = (y + 1 − kx)/4 Choose the right answer

B. x = (y + 1)/(4 + k). y + 1 = 4x + kx = x(4 + k), so x = (y + 1)/(4 + k).

Formulae & algebraic fractions · Ages 13–14

A new subject on both sides or below the line

Clear the denominator, gather it on one side, take it out.

How to do it

Method

Clear the denominator, gather it on one side, take it out

ax = b + cx: x(a − c) = b, x = ba − c

Another way

Check with numbers

y = 3x − 2, x = 5 gives y = 1: 3 + 2 × 11 = 5

In full

A new subject below the line: multiply both sides by that denominator to bring it up. y = 3x − 2: y(x − 2) = 3, xy − 2y = 3, xy = 3 + 2y, x = 3 + 2yy. A new subject on both sides: move every term with it to one side and the rest to the other, take it out as a common factor, then divide by the bracket. ax = b + cx: ax − cx = b, x(a − c) = b, x = ba − c. The factor step can't be skipped: dividing by a alone is wrong. Checking with numbers is the safest end.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
Make x the subject of y = 17x + 3: x = − yy
Fill in each blank
Show the answer and working
Answer: 17, 3
Multiply both sides by x + 3: xy + 3y = 17, xy = 17 − 3y, x = 17 − 3yy.
Example 2
Make x the subject of 7x + 1 = y: x = y −
Fill in each blank
Show the answer and working
Answer: 7, 1
Take 1 from both sides: 7x = y − 1; multiply by x, then divide by y − 1: x = 7y − 1.
Example 3
Which is the formula y = 4x + kx − 1 with x as its subject?
- A. x = y + 14k
- B. x = y + 14 + k
- C. x = y − 14 + k
- D. x = y + 1 − kx4
Choose the right answer
Show the answer and working
Answer: B. x = y + 14 + k
y + 1 = 4x + kx = x(4 + k), so x = y + 14 + k.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.Which is the formula y = 24x with x as its subject?
- A. x = y24
- B. x = 24y
- C. x = 24y
- D. x = 24 − y
Choose the right answer
Answer:
2.Make x the subject of y = 11x + 3: x = − yy
Fill in each blank
Answer:
3.Make x the subject of 15x + 17 = y: x = y −
Fill in each blank
Answer:
4.Which is the formula y = 5x + kx − 11 with x as its subject?
- A. x = y + 115k
- B. x = y − 115 + k
- C. x = y + 11 − kx5
- D. x = y + 115 + k
Choose the right answer
Answer:
5.From y = x + 19x − 7, it follows that x = 7y − 19y − 1.
True or false?
Answer:

All the answers

1. B. x = 24y
2. 11, 3
3. 15, 17
4. D. x = y + 115 + k
5. False

Free worksheet: A new subject on both sides or below the lineWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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