How To Solve Algebraic Equations - 'x' In More Than One Place

Hi, I'm Dr. Shah. I was the National Lector Competition winner in 1989 and I'm the math master at Mathscool.

Now, ready for a new way of doing maths? 8 over X. Okay, so a more complicated equation, x is in more than one place. It's in plenty of places.

First thing I'm going to do is just stick brackets around this subtraction sign at the bottom of the fraction. When we have a fraction, any plus or minus signs in the fraction do have brackets around them.We often don't show it in maths because we get a little bit lazy.

I want to get rid of these denominators at the bottom of the fractions. I'm going to do that by multiplying by each denominator. So the first denominator here is X.

I'm going to multiply by X to get rid of that denominator. So, that divided by X and that multipled by X cancel out. Here, I'm just left with 8.

Here, I'm multiplying by X. When you're multiplying a fraction, you're actually multiplying just the top of the fraction. So the top of the fraction is being multiplied by X.

So we get X squared on the top of the fraction, the bottom doesn't change and here 1 times X is X. I've still got a fraction left, so I want to get rid of this denominator so I'm going to multiply by X minus 5. And that's going to cancel out that denominator, so here I'm going to get 8X minus 5.

That denominator is cancelled out, so I've just got X squared here, and here I get XX minus 5. So now I've got rid of all the denominators. I can cross out that step.

Multiply by denominators, get rid of the fractions. I've done that. Now, I want to multiply out the brackets.

So that's using the arrows that you know to multiply out the brackets. And I'll just restart it up here. So that's 8X minus 40 plus X squared and then, this is X squared and then minus 5X.

So I've multiplied out the brackets. Next step is to simplify, if I can and collect all the X terms together. So I've got an X squared term on this side and an X squared term on this side, so I'm going to take this X squared term and subtract it from both sides.

So subtract X squared from both sides. And you see that the X squared terms cancel out on both sides because you've got an X squared term each side, they just disappear on both sides. And now, I'm going to add 5X to both sides.

That gives me 13X and the minus 5X and the 5X cancel each other out. And then now, I can solve it using a flow diagram so I'll just X times 30 minus 40 is 0. Add 40 to both sides.

That cancels out with that to give me 13x equals 40 and then finally, opposite times 13 is divided by 13. And then, that's that equation finished. So that's how to solve it when X is in more than one place.

You have to follow all these rules. .