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### Course: Algebra (all content) > Unit 2

Lesson 3: One-step addition & subtraction equations- One-step addition & subtraction equations
- One-step addition equation
- One-step addition & subtraction equations
- One-step addition & subtraction equations
- One-step addition & subtraction equations: fractions & decimals
- One-step addition & subtraction equations: fractions & decimals

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# One-step addition equation

In this math lesson, we learn to solve simple equations with one variable. We isolate the variable by removing other terms on the same side. For example, if a + 5 = 54, we subtract 5 from both sides to find a = 49. Finally, we check our solution by substituting the value back into the original equation. Created by Sal Khan.

## Want to join the conversation?

- why is there a pic of queen Elizabeth just chillin'?(81 votes)
- No idea maybe he just thought it'd get our attention, thus leading him to displaying it.(31 votes)

- what do you do if the variable is in the midlle of both numbers for example -10.74=u- (-11)(7 votes)
- Does it help you is you change the equation around?

u-(-11) = -10.74

You can switch the sides of an equation. Now the "u" is not in the "middle" of the numbers. Though, I would argue it was never in the middle of the numbers because the equals symbol is really separating the "u" from the number on the left side.(13 votes)

- How do I fix an equation like 44-q = 11 It's simply a true / false answer in my pre-algebra book. The answer is simple, it's 33. However, I do not know how to configure the equation. The example in the video shows the variable minus the number equals the difference. But what happens when the number is first and the variable is subtracted from the number? How can I configure this equation so that future equations that can not simply be solved without showing the work can be solved?(9 votes)
- You have 2 options...
**Option 1**

Subtract 44 from both sides: -q = -33

Then, you need to divide both sides by -1 to change -q into just q: q = 33**Option 2**

Add q to both sides: 44 = 11 + q

Then subtract 11 from both sides: 33 = q

Hope this helps.(5 votes)

- Why do some numbers get canceled out?(5 votes)
- Some got canceled out because when if you do something like subtraction, you will get 0. If you do division, you will get a 1, and it is already assumed there is a 1 in front of a variable.(9 votes)

- what is the equation for x?

3(x+2)=2(2-x)(4 votes)- 3(x+2)=2(2-x) ...........original equation needs modification to isolate x

3x+6=4-2x ..........distribute

3x+6-6=4-6-2x ......subtract 6 from both sides

3x=-2-2x

3x+2x=-2-2x+2x ......once that is done add 2x to both sides

5x=-2

5x/5=-2/5 ...........divide by 5 on both sides to move the 5 over

x=-2/5(7 votes)

- when we scheck the answer are teacher tough us away longer way to do that(7 votes)
- you said subtract 54 from the right side at 0.59(7 votes)
- why is this different then what the screen shows when you get it wrong and hit the help button?(3 votes)
- This video was made in the old days of Khan academy and this is just how the old formatting of Khan academy was. Takes me back to the old days.(6 votes)

- Is this going to be easy(5 votes)
- why do you need to subtract or add numbers to both sides when you are just getting number off from one side?(3 votes)
- If you just do the operation to one side, the equation is no longer equal (in balance).

For example: 2+5 = 11-4

I've used only numbers so you can see both sides currently = 7. The equation is in balance.

Add 4 to only right side and you get: 2+5 = 11

The equation is no longer equal. I've performed an invalid operation to the equation.

Note: Some teachers teach that you pick up the number and move it to the other side by changing its sign. For example, change the "-4" into "+4" and put it on the left side:

2+5+4 = 11

But, to achieve this, you still have added 4 to both sides. It was just not written out.

Hope this helps.(4 votes)

## Video transcript

Solve for a and
check your solution. And we have a plus
5 is equal to 54. Now, all this is
saying is that we have some numbers,
some variable a. And if I add 5 to
it, I will get 54. And you might be able
to do this in your head. But we're going to do it a
little bit more systematically. Because that'll be
helpful for you when we do more complicated problems. So in general, whenever you
have an equation like this, we want to have the variable. We want this a all by itself
on one side of the equation. We want to isolate it. It's already on
the left-hand side, so let's try to get
rid of everything else on the left-hand side. Well, the only other thing
on the left-hand side is this positive 5. Well, the best way to get rid
of a plus 5, or a positive 5, is to subtract 5. So let's subtract 5. But remember, this says
a plus 5 is equal to 54. If we want the
equality to still hold, anything we do to the left-hand
side of this equation, we have to do to the right
side of the equation. So we also have to
subtract 54 from the right. So we have a plus 5 minus 5. Well, that's just
going to be a plus 0. Because if you add 5 and you
subtract 5, they cancel out. So a plus 0 is just a. And then 54 minus 5, that is 49. And we're done. We have solved for a. A is equal to 49. And now we can check it. And we can check it by
just substituting 49 back for a in our original equation. So instead of writing a
plus 5 is equal to 54, let's see if 49 plus
5 is equal to 54. So we're just
substituting it back in. 49, 49 plus-- let me do that
in that same shade of green. 49 plus 5 is equal to 54. We're trying to check this. 49 plus 5 is 54. And that, indeed,
is equal to 54. So it all checks out.