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CCSS Math: 6.EE.B.7

Solve for x and
check your solution. We have x divided
by 3 is equal to 14. So to solve for x, to figure
out what the variable x must be equal to, we really
just have to isolate it on the left-hand side
of this equation. It's already sitting there. We have x divided
by 3 is equal to 14. We could also write this
as 1/3 x is equal to 14. Obviously, x times 1/3
is going to be x/3. These are equivalent. So how can we just end up with
an x on the left-hand side of either of these equations? These are really the same thing. Or another way, how
can we just have a 1 in front of the x, a 1x,
which is really just saying x over here? Well, I'm dividing
it by 3 right now. So if I were to multiply both
sides of this equation by 3, that would isolate the x. And the reason that would
work is if I multiply this by 3 over here, I'm multiplying
by 3 and dividing by 3. That's equivalent. That's equivalent to
multiplying or dividing by 1. These guys cancel out. Remember, if you do it
to the left-hand side, you also have to do it
to the right-hand side. And actually, I'll do
both of these equations at the same time,
because they're really the exact same equation. So what are we going to get
over here on the left-hand side? 3 times anything divided by 3
is going to be that anything. We're just going to
have an x left over on the left-hand side. And on the right-hand
side, what's 14 times 3? 3 times 10 is 30,
3 times 4 is 12. So it's going to be 42. So we get x is equal to 42. And the same thing
would happen here. 3 times 1/3 is just 1. So you get 1x is equal to
14 times 3, which is 42. Now let's just check our answer. Let's substitute 42 into
our original equation. So we have 42 in place for
x over 3 is equal to 14. So what's 42 divided by 3? And we could do a little
bit of-- I guess we call it medium-long division. It's not really long division. 3 into 4. 3 goes into 4 one time. 1 times 3 is 3. You subtract. 4 minus 3 is 1. Bring down the 2. 3 goes into 12 four times. 3 goes into 42 14 times. So this right over
here simplifies to 14. And it all checks
out, so we're done.