Rearranging Formulas (Where Subject Appears Twice)

This lesson covers:

  1. How to rearrange formulas to change the subject when that variable appears twice
  2. E.g. 'Make x the subject of 5(x - 3) = 4y(1 - 3x)


Make x the subject of the formula:

a=x+32x​
x=\frac{-3a}{a-2}|x=\frac{-3a}{-2+a}|x=\frac{3a}{2-a}

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Make x the subject of the formula:

ba​=x+52x​
x=\frac{5a}{2b-a}|x=\frac{5a}{-a+2b}|x=\frac{-5a}{a-2b}

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Make x the subject of the formula:

x(2+a)=b(x+3)
x=\frac{3b}{2+a-b}|x=\frac{3b}{a-b+2}|x=\frac{3b}{a+2-b}|x=\frac{3b}{2-b+a}|x=\frac{3b}{-b+a+2}|x=\frac{3b}{-b+2+a}

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Make b the subject of the formula:

4(b−2q)=3b+2
b=2+8q|b=8q+2

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Make y the subject of the formula:

v=πy+2y+2a
y=\frac{v-2a}{\pi+2}|y=\frac{v-2a}{2+\pi}|\frac{-2a+v}{\pi+2}|\frac{-2a+v}{2+\pi}|y=\frac{2a-v}{-2-\pi}|y=\frac{2a-v}{-\pi-2}

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Make x the subject of the formula:

2(2p+x)=3−5x
x=\frac{3-4p}{7}|x=\frac{-4p+3}{7}

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Make t the subject of the formula:

y=p−t2pt​
t=\frac{py}{2p+y}|t=\frac{py}{y+2p}|t=\frac{yp}{y+2p}|t=\frac{yp}{2p+y}

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Make b the subject of the formula:

a=b−52−7b​
b=\frac{2+5a}{a+7}|b=\frac{5a+2}{a+7}|b=\frac{2+5a}{7+a}|b=\frac{5a+2}{7+a}

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Make a the subject of the formula:

p=n+an2+a​
a=\frac{n^2-np}{p-1}|a=\frac{-np+n^2}{p-1}|a=\frac{n^2-np}{-1+p}|a=\frac{-np+n^2}{-1+p}|a=\frac{n^2-pn}{p-1}|a=\frac{-pn+n^2}{p-1}|a=\frac{n^2-pn}{-1+p}|a=\frac{-pn+n^2}{-1+p}

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