Explain the difference between the expressions x-3 and 3-x answer
the same as the difference between
-2 and 2
or
-10 and 10
since -(x-3) = 3-x
To understand the difference between the expressions x-3 and 3-x, let's break it down step-by-step:
1. x-3: In this expression, you subtract 3 from the variable x. It means that you start with the value of x and decrease it by 3. For example, if we substitute x with 5, the expression becomes 5 - 3 = 2.
2. 3-x: In this expression, you subtract the variable x from 3. It means that you start with the value of 3 and subtract the value of x from it. For example, if we substitute x with 5, the expression becomes 3 - 5 = -2.
So, the main difference between x-3 and 3-x is in the order of the subtraction. In x-3, you subtract 3 from x, while in 3-x, you subtract x from 3. This change in the order of subtraction produces different results when you substitute different values for x.
To understand the difference between the expressions x-3 and 3-x, let's break down each expression individually:
1. x-3: This expression represents subtracting 3 from the variable x. In other words, if you have a value for x, you would subtract 3 from it.
2. 3-x: This expression represents subtracting the variable x from 3. In this case, regardless of the value of x, you would subtract x from 3.
Now, let's consider a few scenarios to see how the expressions differ:
Scenario 1: If x = 5
- In the expression x-3, substituting x=5, we get 5-3 = 2.
- In the expression 3-x, substituting x=5, we get 3-5 = -2.
Scenario 2: If x = -2
- In the expression x-3, substituting x=-2, we get -2-3 = -5.
- In the expression 3-x, substituting x=-2, we get 3-(-2) = 3+2 = 5.
From these examples, we can observe that the main difference arises from the order of the subtraction operation. In x-3, it means subtracting 3 from x, whereas in 3-x, it means subtracting x from 3.
In summary, the expressions x-3 and 3-x differ in the order of subtraction, which can result in different values depending on the given variable x.