Changing The SubjectChange the subject in formulae in which the new subject appears twice. 
Make \(x\) the subject of each formula given below then drag the equivalent solution to the answer panel. There are spaces where you can show your working (see the Help tab for more information)
$$ axb=cx $$  $$ ax+b=cx+d $$  $$ a(xb)=c(dx) $$ 
$$ a(3x)=5x $$  $$ a= \frac{cx  b}{x} $$  $$ x+c=abx $$ 
$$ a = \frac{bx}{x+c} $$  $$ \frac{axc}{b+x} = d $$  $$ a = \sqrt{ \frac{x+10}{x} } $$ 
$$ \frac{5b}{2x} = \frac{c + b}{xe} $$  $$ ( \frac{x^2  10}{x^2 + 10} )^2 = a $$  $$ \frac{1}{x} ( \frac{ax}{c} +b) = 10d $$ 
\(x= \frac{b}{ac}\)
\(x= \frac{db}{ac}\)
\(x= \frac{ab+cd}{a+c}\)
\(x= \frac{3a}{a+5}\)
\(x= \frac{b}{ca}\)
\(x= \frac{ac}{b+1}\)
\(x= \frac{ac}{ba}\)
\(x= \frac{db+c}{ad}\)
\(x= \frac{10}{a^21}\)
\(x= \frac{5be}{3b2c}\)
\(x= \sqrt{\frac{10(1+\sqrt{a})}{1\sqrt{a}}}\)
\(x= \frac{bc}{10cda}\)
CONGRATULATIONS !
All of the formulae are in the correct places. Well done.
Claim your trophy using the button below.
At least two of your formulae are in the wrong places. Check your working carefully and ask your teacher for help.
Try again.
This is Changing The Subject level 8. You can also
try:
Level 1
Level 2
Level 3
Level 4
Level 5
Level 6
Level 7
Examstyle Questions
Close
Level 1  Formulas which can be rearranged by adding or subtracting terms from both sides
Example: Make e the subject of the formula d = e  f
Level 2  Formulas which can be rearranged by multiplying or dividing both sides by a value
Example: Rearrange the formula n = mp
Level 3  Formulas which can be rearranged by adding, subtracting, multiplying or dividing both sides by a value
Example: Rearrange the formula b = a + cd
Level 4  Formulas including brackets or expressions in the numerator or denominator of a fraction
Example: Rearrange the formula p = s(t + 2)
Level 5  Formulas including squares or square roots
Example: Rearrange the formula d² = 2a + 1
Level 6  Finding the unknown which is not the subject of a formula
Example: If m = n² + 2p, find p when m=8 and n=10
Level 7  Rearrange the formulae where the new subject appears twice; fill in the blanks
Example: Rearrange the formula ax + b = cx + g to make x the subject
Level 8  Rearrange the formulae where the new subject appears twice; show your working
Example: Rearrange the formula a(3x)=5x to make x the subject
Exam Style Questions  A collection of problems in the style of GCSE or IB/Alevel exam paper questions (worked solutions are available for Transum subscribers).
More Algebra including lesson Starters, visual aids, investigations and selfmarking exercises.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
See the National Curriculum page for links to related online activities and resources.
Make \(x\) the subject of the following formula:
$$ a = \frac{bx}{2x+c} $$Multiply both sides of the equation by \(2x+c\)
$$ 2ax + ac = bx $$Add \(x\) and subtract \(ac\) from both sides
$$ 2ax + x = b  ac $$Factorise the left side
$$ x(2a + 1) = b  ac $$Divide both sides by \(2a + 1\)
$$ x= \frac{b  ac}{2a + 1} $$In the boxes made available to show working the following formatting shortcuts may be useful.
Fractions: use the forward slash / (use brackets to group together multiple term numerators)
Indices: use the up arrow key ^ then type the index.
Square root: type \sqrt followed by a space
+ The blue button allows you to add extra lines of working.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
Close


Transum.orgThis web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available. Please contact me if you have any suggestions or questions. 
More Activities: 

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the 1 August 'Starter of the Day' page by Peter Wright, St Joseph's College: "Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities. Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology: "This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative." 
Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month. The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing. Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page. 

AnswersThere are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer. A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves. Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members. If you would like to enjoy adfree access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now: Subscribe 

Go MathsLearning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths main page links to more activities designed for students in upper Secondary/High school.  
Teachers  
If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows: 
Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes. 
It may be worth remembering that if Transum.org should go offline for whatever reason, there are mirror sites at Transum.com and Transum.info that contain most of the resources that are available here on Transum.org. When planning to use technology in your lesson always have a plan B! 
Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments. 