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Lesson 4: One-step addition and subtraction equations

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.

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• why is there a pic of queen Elizabeth just chillin'?
• No idea maybe he just thought it'd get our attention, thus leading him to displaying it.
• Instead of all the extra steps you can literally just do it backwards.
54 - 5 = a
a = 49

49 + 5 = 54
• Yea, you are absolutely right.
• what do you do if the variable is in the midlle of both numbers for example -10.74=u- (-11)
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.
• If b + 10 = 109, we subtract 10 from both sides to find b = 99.
• 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?
• 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.
• Am i color blind? or is Sal? because he keeps saying in his videos "this shade of green" and i see yellow.... not green...
• There is some color variation between computer screens. On Sal's system, it may look more green than on yours.
• Why do some numbers get canceled out?
• 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.
• what is the equation for x?
3(x+2)=2(2-x)
• 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
• when we scheck the answer are teacher tough us away longer way to do that
• A= 49 ez

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.