Order of operations

[khris le]

Hi can someone tell me the order of operations specifically when solving for x for different algebraic equations? Is it different to the usual bodmas?

 

[Deleted member 4993]

Hi can someone tell me the order of operations specifically when solving for x for different algebraic equations? Is it different to the usual bodmas?

The short answer is - NO. But it will be useful if you post a problem where you are having doubts.

 

[khris le]

These are the questions i'm talking about. Would I do the division/multiplication first or the addition/subtraction?

 

[Dr.Peterson]

Hi can someone tell me the order of operations specifically when solving for x for different algebraic equations? Is it different to the usual bodmas?

The order of operations is always the same; that refers to evaluating an expression. What changes is what you are doing: In solving, you are commonly "undoing" operations, which you do in reverse order.

I compare it to the "order of operations" in getting dressed. You put on your socks first, then your shoes. But in taking them off, you take off the shoes first, then the socks. (Actually, you can take off the socks first, but it hurts your fingers and stretches the sock, so it isn't recommended. The same is true in algebra!)

The point is, the rule doesn't change, because it's an order of doing operations; you're just using it backwards.

 

[khris le]

but I can get a different answer depending on which operation I undo first so sometimes I get the answer wrong.....

 

[Dr.Peterson]

but I can get a different answer depending on which operation I undo first so sometimes I get the answer wrong.....

As you were asked, please show an example, so we can see where you are making a mistake. When you undo things in a different order, you have to be very careful to do them legally. It's hard to diagnose a problem when you don't show us where it hurts.

 

[khris le]

As you were asked, please show an example, so we can see where you are making a mistake. When you undo things in a different order, you have to be very careful to do them legally. It's hard to diagnose a problem when you don't show us where it hurts.

I posted one 26 mins ago but it said that message is still waiting for approval

 

[khris le]

As you were asked, please show an example, so we can see where you are making a mistake. When you undo things in a different order, you have to be very careful to do them legally. It's hard to diagnose a problem when you don't show us where it hurts.

Here's one 3-(4x/5) = 11 or (2+5x/7) = 6

 

[Dr.Peterson]

Here's one 3-(4x/5) = 11 or (2+5x/7) = 6

I see post #3 now. But, again, we need to see you WORK in order to know what you are doing wrong.

View attachment 32122

These are the questions i'm talking about. Would I do the division/multiplication first or the addition/subtraction?

Each can be done in a couple different ways; but, for example, if you do #2 by multiplying first, you need to be sure to multiply every term; subtraction first is more direct. I could guess what mistakes you might be making, but it's better to see the reality.

 

[pka]

Here's one 3-(4x/5) = 11 or (2+5x/7) = 6

In both cases I would deal with the fractions first.
[imath]5\{3-\left[\dfrac{4x}{5}\right]\}=5(11)\\15-4x=55[/imath]

[imath][/imath][imath][/imath][imath][/imath]

 

[Dr.Peterson]

Each can be done in a couple different ways; but, for example, if you do #2 by multiplying first, you need to be sure to multiply every term; subtraction first is more direct.

I'll demonstrate a couple ways #2 could be done:

Following the order of operations in reverse, starting with [imath]\frac{x}{5}+3=5[/imath], we would first undo the last operation on the left (addition) by subtracting 3 from both sides; we get [imath]\frac{x}{5}=2[/imath]. Next we would undo the remaining operation (division) by multiply both sides by 5: [imath]5\cdot\frac{x}{5}=5\cdot2[/imath], so that [imath]x=10[/imath].

Often we prefer (as pka showed) to clear fractions first, largely because working with fractions is more error-prone. This time, starting with [imath]\frac{x}{5}+3=5[/imath], we would first multiply both sides by 5. But that means we multiply the entire left side and the entire right side by 5, which many beginners forget to do. That is, we are doing this: [imath]5\left[\frac{x}{5}+3\right]=5[5][/imath]. Distributing on the left, this becomes [imath]5\cdot\frac{x}{5}+5\cdot3=5\cdot5[/imath]; we've multiplied every term. Carrying this out leaves [imath]x+15=25[/imath]. Now we undo the remaining operation (addition) by subtracting 15 from both sides, leaving [imath]x=10[/imath].

We get the same result both ways, as long as we do the work correctly. In some cases, as in #5, clearing fractions is the same as following the reverse order of operations, because the last operation performed in evaluating is the division, so you undo that first anyway.