How To Add Linear Fractions

we have the equation negative16 is equal to x over 4, plus 2. and we need to solve for x. so we really just need toisolate the x variable on one side of this equation, and thebest way to do that is first

How To Add Linear Fractions, to isolate it-- isolate thiswhole x over 4 term from all of the other terms. so in orderto do that, let's get rid of this 2. and the best way to get rid ofthat 2 is to subtract it.

but if we want to subtract itfrom the right-hand side, we also have to subtract it fromthe left-hand side, because this is an equation. if this is equal to that,anything we do to that, we also have to do to this. so let's subtract 2from both sides. so you subtract 2 from theright, subtract 2 from the left, and we get, on theleft-hand side, negative 16 minus 2 is negative 18.

and then that is equalto x over 4. and then we have positive 2minus 2, which is just going to be 0, so we don't evenhave to write that. i could write just a plus 0,but i think that's a little unnecessary. and so we have negative 18is equal to x over 4. and our whole goal here isto isolate the x, to solve for the x. and the best way we can dothat, if we have x over 4

here, if we multiply thatby 4, we're just going to have an x. so we can multiply thatby 4, but once again, this is an equation. anything you do to theright-hand side, you have to do to the left-hand side,and vice versa. so if we multiply the right-handside by 4, we also have to multiply the left-handside by 4. so we get 4 times negative 18 isequal to x over 4, times 4.

the x over 4 times 4,that cancels out. you divide something by 4 andmultiply by 4, you're just going to be left with an x. and on the other side,4 times negative 18. let's see, that's 40. well, let's just write it out. so 18 times 4. if we were to multiply 18 times4, 4 times 8 is 32. 4 times 1 is 4, plus 1 is 72.

but this is negative 18 times4, so it's negative 72. so x is equal to negative 72. and if we want to check it, wecan just substitute it back into that original equation. so let's do that. let's substitute this intothe original equation. so the original equation wasnegative 16 is equal to-- instead of writing x, i'm goingto write negative 72-- is equal to negative72 over 4 plus 2.

let's see if this isactually true. so this right-hand sidesimplifies to negative 72 divided by 4. we already know that thatis negative 18. so this is equal to negative18 plus 2. this is what the equationbecomes. and then the right-hand side,negative 18 plus 2, that's negative 16. so it all comes out true.

this right-hand side, when x isequal to negative 72, does indeed equal negative 16.