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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)
| $$ ax-b=cx $$ | $$ ax+b=cx+d $$ | $$ a(x-b)=c(d-x) $$ |
| $$ a(3-x)=5x $$ | $$ a= \frac{cx - b}{x} $$ | $$ x+c=a-bx $$ |
| $$ a = \frac{bx}{x+c} $$ | $$ \frac{ax-c}{b+x} = d $$ | $$ a = \sqrt{ \frac{x+10}{x} } $$ |
| $$ \frac{5b}{2x} = \frac{c + b}{x-e} $$ | $$ ( \frac{x^2 - 10}{x^2 + 10} )^2 = a $$ | $$ \frac{1}{x} ( \frac{ax}{c} +b) = 10d $$ |
\(x= \frac{b}{a-c}\)
\(x= \frac{d-b}{a-c}\)
\(x= \frac{ab+cd}{a+c}\)
\(x= \frac{3a}{a+5}\)
\(x= \frac{b}{c-a}\)
\(x= \frac{a-c}{b+1}\)
\(x= \frac{ac}{b-a}\)
\(x= \frac{db+c}{a-d}\)
\(x= \frac{10}{a^2-1}\)
\(x= \frac{5be}{3b-2c}\)
\(x= \sqrt{\frac{10(1+\sqrt{a})}{1-\sqrt{a}}}\)
\(x= \frac{bc}{10cd-a}\)
CONGRATULATIONS !
All of the formulae are in the correct places. Well done.
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At least two of your formulae are in the wrong places. Check your working carefully and ask your teacher for help.
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This is Changing The Subject level 8. You can also
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Exam-style Questions
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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(3-x)=5x to make x the subject
Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).
More Algebra including lesson Starters, visual aids, investigations and self-marking 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:
$$ a = \frac{b-x}{2x+c} $$Multiply both sides of the equation by \(2x+c\)
$$ 2ax + ac = b-x $$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.
These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.
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