(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

like numbers, and our answer

is an expression.