Here we will learn about making x the subject of an equation or a formula.
There are also rearranging equations worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
Making x the subject of a formula or equation means rearranging the equation or formula so that we have a single x variable equal to the rest of it.
Make x the subject.
In order to make x the subject:
E.g. factorise 2x + 3xy to x(2+3y)
*not always required*
Get your free make x the subject worksheet of 20+ questions and answers. Includes reasoning and applied questions.
Get your free make x the subject worksheet of 20+ questions and answers. Includes reasoning and applied questions.
Make x the subject.
Step 1:
Divide each side of the equation by 3
Step 2:
Subtract a from each side of the equation
Step 1:
Subtract t from both sides of the equation
Step 2:
Square root each side
Remember the square root can be + or \;−
Step 1:
Add 9a to both sides of the equation
Step 2:
The inverse operation of ‘square root’ is to ‘square’ each side
Step 3:
The inverse operation of multiply is divide, so divide both sides by 5
Step 1:
Multiply each side of the equation by the denominator
Step 2:
Expand the bracket on the left hand side of the equation and rearrange the equation. This will help us to get all terms with x onto one side of the equation
Step 3:
Factorise the left side of the equation so we have a single variable x.
Step 4: Divide by (a - 5b)
This will leave x as the subject of the equation
Step 1:
Multiply each side of the equation by the denominator of the other side.
Step 2:
Expand the bracket on the LHS and RHS of the equation and rearrange. This will help to get all terms with x onto one side of the equation
Step 3:
Factorise the left side of the equation so that we are left with only one of the variable x.
Step 4:
Divide both sides by (b + 8) to leave x as the subject
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.
To isolate the variable x we need to multiply both sides by 2.
This is wrong because we have only multiplied the 3y by 2.
The correct answer should be:
This is correct because we have multiplied everything by 2 using brackets.
E.g.
To isolate the variable x from 5x we need to perform the inverse operation.
5x = 5 × x , so the inverse operation is divide by 5 .
\[\fracso the inverse operation is × 5.
E.g.
To isolate the variable x from x+5 we need to perform the inverse operation:
The inverse operation of +5 is −5.
E.g.
To isolate the variable x from x−5 we need to perform the inverse operation:
The inverse operation of −5 is +5.
To make x the subject there can only be one x visible at the end. We need to get all x ’s on one side of the equal sign and then factorise.
\[\beginWhen we square rooting a number/variable as an inverse operation the answer can be positive or negative.
\begin & ^>=4 \\ & x=\pm \sqrt=\pm 2 \\ \end \[\sqrt1.Make x the subject of the formula.
Divide both sides by 6
Then subtract 8 from both sides
2.Make x the subject of the formula.
Add 4b to both sides
Square root both sides
3. Make x the subject of the formula.
Square both sides
Add 8 to both sides
Divide both sides by 7
4.Make x the subject of the formula.
Multiply both sides by 5x
Subtract 4x from both sides
Factorise the left hand side
Divide both sides by the quantity in the bracket
5. Make x the subject of the formula.
Multiply each side of the equation by the denominator of the other side.
To both sides, add 6x and subtract 3y
Factorise the left hand side
Divide by the quantity in the bracket
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You have now learned how to:
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