If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:6:04

we have the equation negative nine minus this whole expression 9x minus six this whole thing is being subtracted from negative nine is equal to three times this whole expression 4x plus 6 now a good place to start is to just get rid of these parenthesis and the best way to get rid of these parenthesis is to kind of multiply them out this has a negative one you just see an minus here but it's really the same thing as having a negative one times this quantity and here you have a 3 times this quantity so let's multiply it out using the distributive property so the left-hand side of our equation we have our negative 9 and then we want to simply want to multiply the negative 1 times each of these terms so negative 1 times 9x is negative 9x and then negative 1 times negative 6 is plus 6 or positive 6 and then that is going to be equal to let's distribute the 3 3 times 4x is 12x and then 3 times 6 is 18 3 times 6 is 18 now what we want to do let's combine our constant terms if we can we have a we have a negative 9 and a 6 here on this side we've combined all of our like terms we can't combine a 12x and an 18 so let's combine this so let's combine the negative 9 and the 6 our two constant terms on the left-hand side of the equation so we're going to have a we're going to have this negative 9x so we're going to have negative 9x plus or plus well see we have a negative 9 and then plus 6 so negative 9 plus 6 is negative 3 so we're going to have a negative 9x and then we have a negative 3 so minus 3 right here that's the negative 9 plus the 6 and that is equal to 12x plus 18 now we want to group all of the X terms on one side of the equation and all of the constant terms a negative 3 and the positive 18 on the other side I like to always have my X terms on the left hand side if I can you don't have to have them on the left so let's let's do that so if I want all my X terms on the Left I have to get rid of this 12x from the right and the best way to do that is to subtract 12 X from both sides of the equation so let me subtract 12x from the right and subtract 12x from the left now on the left hand side I have negative 9x minus 12x so negative 9 minus 12 that's negative 21 negative 21 X minus 3 is equal to 12x minus 12x well that's just nothing that's zero so I could write a 0 here but I don't have to write anything that was a whole point of subtracting the 12x from the left-hand side and that is going to be equal to so on the right hand side we just are left with an 18 we are just left with that 18 here these guys cancelled out now let's get rid of this negative 3 from the left hand side so on the left hand side we only have X terms on the right hand side we only have constant terms so the best way to cancel out a negative 3 is to add 3 so it cancels out to 0 so we're going to add 3 to the left let's add 3 to the right and we get the left hand side of the equation we have the negative 21x no other X term to add or subtract here so we have negative 21 X the negative 3 and the plus 3 or the positive 3 cancel out that was the whole point equals what's 18 plus 3 18 plus 3 is 21 is 21 so now we have negative 21 X is equal to 21 and we want to solve for x so if you have something times X and you just want it to be an X let's divide by that something and in this case that something is negative 21 so let's divide both sides of this equation by negative 21 divide both sides by negative 21 the left-hand side negative 21 divided by negative 21 you're just left with an X that was the whole point behind dividing by negative 21 and we get X is equal to what's 21 divided by negative 21 well that's just negative 1 right you have the positive version divided by the negative version of itself so it's just negative 1 so that is our answer that is our answer now let's verify that this actually works for that original equation so let's substitute negative 1 into that original equation so we have negative 9 do it over here I'll do it in a different color than we've been using we have negative nine minus that one wasn't there originally it's there implicitly minus nine times negative one nine times I'll put negative one in parenthesis minus six is equal to well actually let me just solve for the left hand side so when I subtract when I substitute a negative one there so the left-hand side becomes negative nine minus nine times negative one is negative nine minus six and so this is negative nine minus in parentheses negative nine minus six is negative 15 so this is equal to negative fifteen and so we get negative nine let me make sure I did that negative nine minus six yep negative fifteen so I have negative nine minus negative fifteen that's the same thing as negative nine plus 15 which is six so that's what we get on the left-hand side of the equation when we substitute X is equal to negative one we get it is equal six so let's see what happens when we substitute negative 1 to the right-hand side of the equation I'll do it in green we get three times four times negative one four times negative one plus six and so that is three times negative four plus six negative four plus six is two so it's three times two which is also six so when X is equal to negative one you substitute here the left-hand side becomes six and the right-hand side becomes six so this definitely works out