The difference of a number and 5 is at most 20 x -5> 20 x -5 greater = 20 right
x - 5 ≤ 20
"at most" means it can't go over 20, so it has to be less than.
Your expression said > 20
Furthermore, by saying the difference between a number and 5, you don't say which way we are subtracting.
e.g. if I say what is the difference between 2 and 10 you would probably say 8, without really caring that 10-2 = 8 but 2 - 10 = -8
so the correct answer would be
|x - 5| ≤ 20
To find the difference between a number and 5, we need to subtract 5 from the number. If the difference is at most 20, it means the result of subtracting 5 from the number should be less than or equal to 20.
So, the inequality expression to represent this situation would be: x - 5 ≤ 20.
Now, let's solve this inequality to find the possible values of x:
Add 5 to both sides of the inequality to isolate the variable x:
x - 5 + 5 ≤ 20 + 5
This simplifies to: x ≤ 25.
Therefore, the answer is x is less than or equal to 25, not greater than.