**Recognise When x Satisfies an Equation with Decimals** *KS3 Revision*

## 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:

y=4x-13

3=4\times4-13

3=16-13

3=3

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=x+6

8.9=2.9+6

8.9=8.9

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?*

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=6.4

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.

## Example Questions

**Question 1:** *Does x=3.7 satisfy the equation 5.7=2+x?*

5.7=2+x

5.7=2+3.7

5.7=5.7

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

**Question 2:** *Does x=6.4 satisfy the equation 9.8=x+3.5?*

9.8=x+3.5

9.8=6.4+3.5

9.8=9.9

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