## Formulas – Multi-Step Formulas – YouTube.mp4

(male narrator)
In this video, we will continue solving
formulas; this time solving
multistep formulas. Our strategy
is still going to be exactly the same
as before. We will solve these
multistep formulas the same… as linear equations. As we do, we will treat all
other variables like numbers, and our final answer
will be an expression. So let’s try an example here
solving this formula for x. If all of the other letters
were numbers… what we
would do first would be to take care of the
number in front of parentheses. There are two ways
we can do this. The most common way
that we’ve done before is to distribute the a
through the parentheses. This gives us 3xa,
plus ab, equals by. Now that the parentheses
are gone, we’re ready to start solving
for the x. Notice, the second term
has no x’s on it. That’s what’s added
to the x term. As with other
two-step equations, we do the adding
and subtracting first. The opposite of adding ab
is subtracting ab, and we always do things
on both sides of the equation. With the ab’s gone, we’re left
with 3xa on the left side. On the right side,
it’s important to note that these are not like terms
and cannot be combined. So we leave it as a subtraction
problem: by minus ab. Now, we are ready
to get our variable alone. Remember, we’re solving
for x, so we need to divide out
the other factors: divide out a 3
and divide out an a. Doing the same thing
to both sides, and the 3s and a’s divide out,
leaving just the x behind. x is now alone, and it’s
equal to the expression: by minus ab,
over 3a. It is important to note
that although we have an a in the denominator
and the numerator, we cannot divide
the a out because of the subtraction
in the problem. If there is any adding
or subtracting in a fraction, we cannot do
any reducing. Let’s try
another example. In this next problem, you’ll notice we also have
parentheses that need
to be dealt with first. Again, we
will distribute through the parentheses
as we begin. This gives us 3a plus 6b,
plus 5b, equals -2a, plus b. As usual,
after distributing, we can check
to combine like terms. On the left side
of the equation, you’ll notice
there’s 6b plus 5b. When we combine those,
we now have 3a plus 11b. The right side
is still -2a plus b. Remember, we’re solving
this equation for a. Notice the a is on both sides
of this equation. Just as before, we will get
all the a’s on the same side by moving
the smaller term. The -2 is smaller than the +3,
so we will move that one. The opposite of subtracting 2
is adding 2a to both sides. As we do, we line up
the like terms, and we now have 5a… plus 11b… equals b. We solve
this two-step equation first by getting rid
of the term without a. The opposite of plus 11b
is minus 11b. This time, you notice
that on the right side, we have like terms
that can be combined. We now have
5a equals -10b. To get the a alone, we simply
have to get rid of the 5 by dividing both sides
by the 5. The 5s divide out, and we’re left
with a equals -2b. As we solve these formulas,
we remember that we treat the other variables