Question

How does the order of operations relate to solving multi-step equations? Use examples of solving an equation, and then evaluating it to help in your explanation.

Answer 1

Multi-step equations must be solved using the order of operations or they will give multiple different answers.

Here's an example.

2(x+1)=6

Go out of order and subtract the 1 first.
Perhaps it would look something like this.

2(x+1)=6
-1 -1
2x = 5

Then, divide by 2 on each side. I am going to multiply by 1/2 since I don't have a good way to show a division line.

(1/2)(2x)=5(1/2)
x=5/2 or x=2.5

Correctly, the solution does the multiplication required by the parentheses on the left first.

2(x+1)=6
2x+2=6
Now, we can subtract the two from each side.

2x+2=6
-2 -2
2x=4

Now divide by 2 on each side. I will multiply by 1/2 for ease of typing.
(1/2)(2x)=4(1/2)
x=2

Both 2 and 2.5 cannot be the solution. The order-of-operation rules allow every person to get the same answer and let math be "true."