## 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!