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.
Question 1: Does x=3.7 satisfy the equation 5.7=2+x?
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?
Close but no cigar! 9.8 does not equal 9.9, so x=6.4 does not satisfy the equation!
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