Hey, everyone. As you solve a bunch of different linear equations, you may come across a linear equation that has fractions in it. Now I know that fractions can be scary and sometimes a little bit challenging to work with, but don't worry, we're going to get rid of these fractions as quickly as possible and get back to a linear equation that looks exactly like what you've already been solving. So when we see a linear equation with fractions, we need to eliminate those fractions using the least common denominator. So let's look at that in an example.
So we want to solve this equation, and it says 14 ∗ x + 2 - 13 ∗ x = 112. Now this equation definitely has fractions in it, and I want to get rid of those as soon as possible. So here, we're actually adding a step 0 before we do anything else. And our step 0 is going to be to multiply by our LCD, our least common denominator, in order to eliminate our fractions. So looking at my equation here, my denominators are 4, 3, and 12. So my least common denominator here is going to be 12. So, to get rid of those fractions, I need to multiply my entire equation by 12. When we multiply by our least common denominator, we want to make sure to distribute it to every single term in our equation.
So let's go ahead and simplify this. I have 124 ∗ ( x + 2 ) - 123 ∗ x = 1212. Now we can even simplify this a little bit further. So if I take 12 divided by 4, that gives me 3 times (x+2) minus 4x equals 1. Now all of my fractions are gone and I can continue solving this just as I would any other linear equation. So my step 0 is done.
I can move on to step 1 which is to distribute our constants. Now looking at this, I have this 3 here that needs to get distributed to both the x and my 2. So that gives me 3x+6. We don't have anything to distribute there. So step 1 is done. Now step 2 is to combine like terms. So looking at my equation, I have a couple of like terms. I have 3x and negative 4x, and those are going to combine to give me negative one x. Everything else is going to stay the same. So I still have that plus 6 equals 1. So step 2 is done.
I have combined my like terms. Now looking at step 3, I want to group my terms with x on one side and constants on the other to get them on opposite sides. So I'm going to go ahead and move this 6 over to the other side in order to get all my constants on one side. So, in order to do that I'm just going to subtract 6 from both sides. And here, it will cancel, and my negative one x stays there. And then I have 1 minus 6, which will give me negative 5. So I've completed step 3. I have moved my constants, moved my x terms to be on opposite sides. Now I want to do step 4, which is to isolate x.
Now I just have a negative one multiplying my x. So, in order to get rid of that negative one, I need to divide by it on both sides. So it will cancel over here, and I am left with x equals negative 5 divided by negative 1 gives me positive 5, and this is my solution. So I've completed step number 4. Now step number 5, again, is to check by replacing x in our original equation. Now when we have fractions in our equation, this can get a little bit complicated and sometimes be time-consuming, so this step is optional. But remember, you can always put it back in your original equation to double-check. That's all for this one, guys, thanks for watching.