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In order to access this I need to be confident with:
Expanding brackets Factorising Solving equationsThis topic is relevant for:
Here we will learn about making
There are also rearranging equations worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if youβre still stuck.
Making
For example,
Make
Step-by-step guide: Rearranging equations
In order to make
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When we perform an operation to the left hand side of the equation we have to perform the same operation to the right hand side.
E.g
To isolate the variable
This is wrong because we have only multiplied the
The correct answer should be:
This is correct because we have multiplied everything by 2 using brackets.
E.g.
To isolate the variable
E.g.
so the inverse operation is Γ 5.
E.g.
To isolate the variable
The inverse operation of +5 is β5.
E.g.
To isolate the variable
The inverse operation of β5 is +5.
To make
E.g.
When we square rooting a number/variable as an inverse operation the answer can be positive or negative.
E.g.
1.Make x the subject of the formula.
y = 6(x+8)
x = y – \frac{3}{4}
x = \frac{y}{6} + 8
x = \frac{y}{6} – 8
x = y – 8
Divide both sides by 6
\frac{y}{6} = x + 8
Then subtract 8 from both sides
x = \frac{y}{6} – 8Β
2.Make x the subject of the formula.
3p={x}^2-4bΒ
x=\pm\sqrt{3b+4p}
x=\pm\sqrt{4b-3p}
x=4b+3p
x=\pm\sqrt{4b+3p}
3p={x}^2-4b
Add 4b to both sides
3p+4b=x^{2}
Square root both sides
x=\pm\sqrt{4b+3p}
3. Make x the subject of the formula.
6g=\sqrt{7x-8}
x=\frac{6{g}^2+8}{7}
x=\frac{36{g}^2-8}{7}
x=\frac{36{g}^2+8}{7}
x=\frac{6g+8}{7}
6g=\sqrt{7x-8}
Square both sides
(6g)^{2}=(\sqrt{7x-8})^{2}
36g^{2}=7x-8
Add 8 to both sides
36g^{2}+8=7x
Divide both sides by 7
x=\frac{36{g}^2+8}{7}
4.Make x the subject of the formula.
y=\frac{4x-f}{5x}
x=\frac{f}{5y-4}
x=\frac{-f}{5y+4}
x=\frac{f}{5y+4}
x=\frac{-f}{5y-4}
y=\frac{4x-f}{5x}
Multiply both sides by 5x
5xy=4x-f
Subtract 4x from both sides
5xy-4x=-fΒ
Factorise the left hand side
x(5y-4)=-fΒ
Divide both sides by the quantity in the bracket
x=\frac{-f}{5y-4}
5. Make x the subject of the formula.
\frac{y}{3}=\frac{6-2x}{x+3}
x=\frac{18+3y}{y+6}
x=\frac{18-3y}{y-6}
x=\frac{18-3y}{y+6}
x=\frac{18+3y}{y-6}
\frac{y}{3}=\frac{6-2x}{x+3}
Multiply each side of the equation by the denominator of the other side.
xy+3y=18-6x
To both sides, add 6x and subtract 3y
xy+6x=18-3y
Factorise the left hand side
x(y+6)=18-3y
Divide by the quantity in the bracket
x=\frac{18-3y}{y+6}
1. Make x the subject of the formula
y=5x-7
(2 marks)
y+7=5xΒ
(1)
\frac{y+7}{5} = x
(1)
2. Make x the subject of the formula
z^{2}=x^{2}-5 a y
(2 marks)
z^{2}+5 a y=x^{2}
(1)
\pm\sqrt{z^{2}+5 a y}=x
(1)
3. Make x the subject of the formula
y=\frac{3(t+5 x)}{x}
(4 marks)
y x=3 t+15 x
(1)
y x-15 x=3 t
(1)
x(y-15)=3 t
(1)
x=\frac{3t}{y-15} \quad
(1)
You have now learned how to:
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