Recognise When x Satisfies an Equation with Decimals| KS3 Maths

What you need to know

Things to remember:

  • To see if something “satisfies” something else in maths, it just means to check that it works or is true.
  • We use substitution to see if values satisfy an equation.
  • We can split up a decimal number into the “whole number” part and the “decimal” part.

We’ve seen how to check if values satisfy and equation before, so let’s recap.

Do x=4 and y=3 satisfy the equation y=4x-13?


To see if these values satisfy the equation, all we have to do is substitute them in. We can do this with one of two methods:





We can check if decimal number satisfy an equation in the same way.


Does x=2.9 satisfy the equation 8.9=x+6?

Hint: Remember, when we add a whole number to a decimal number, we just need to add the whole number parts. The decimal doesn’t change.





8.9 does equal 8.9, so x=2.9 satisfies the equation!

Things get a little trickier when there is another decimal number, but we can make the questions a little easier by splitting up the second decimal into “whole number” and “decimal” parts.

Does x=5.6 satisfy the equation 8.9=9.3-x?


Start by substituting as usual.

8.9=9.3 - 2.9

Now split up the second decimal into “whole number” and “decimal” parts.

8.9=9.3 - 2 - 0.9

Now just do the two subtractions one at a time.

8.9=9.3 - 2 - 0.9

8.9=7.3 - 0.9


8.9 does not equal 6.4, so x=5.6 does not satisfy the equation.

We can use the same technique when adding two decimals.

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Example Questions




5.7 does equal 5.7, so x=3.7 satisfies the equation!







Close but no cigar! 9.8 does not equal 9.9, so x=6.4 does not satisfy the equation!

KS3 Maths Revision Cards

KS3 Maths Revision Cards

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