Main content

### Course: 7th grade (Illustrative Mathematics) > Unit 6

Lesson 4: Lesson 9: Dealing with negative numbers# Worked example: two-step equations

Sal solves the equation -16 = x/4 + 2. It takes two steps because he first has to subtract 2 from both sides and then multiply both sides by 4. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- cant you just solve this equation by doing the whole thing backwards instead of doing all of this stuff? otherwise, is there a simpler way to solve this(54 votes)
- he kind of overcomplicated this.(1 vote)

- Here is an example:)

Marta gets paid $15 for each sale, plus a base salary of $250 per week. Marta wants to earn $550 this week.

How many sales must she make?

Define a variable for the unknown.

Let x = number of sales

Write an expression that models the problem (in this case, how Marta's weekly pay is calculated).

15x + 250

Set the expression equal to the final result.

15x + 250 = 550(25 votes)- X=20, this is the correct answer(1 vote)

- In this example, why would we divide first then subtract? 30=5(x+1)(10 votes)
- Use the order of operations (or GEMS): Grouping symbols, Exponents, Multiplicatives (Multiplying and dividing), and Subtractives (Subtraction and addition)(3 votes)

- What if there are two variables on one side, ( e.g. -20=-4x-6x)(6 votes)
- If they are the same variables, just add or subtract them to get -4x - 6x = -10x. Then your equation simplifies to -20 = -10x → x = 2.(8 votes)

- Anyone knows why we have to subtract on both sides(4 votes)
- An equation acts like the scale/balance in science class. To keep the scale in balance, we always do the same operation to both sides of the equation when we move items across the equals symbol.

There are videos on this back in the lessons on 1-step equations.

Hope this helps.(9 votes)

- How would you do -11b+7=40 ?(4 votes)
- Two steps: Closest to the b is multiply by -11 and then add 7, so going backwards, subtract 7 from both sides and divide by -11. (40-7)/(-11).(7 votes)

- so if i am correct for the problem -4(w+1) = -24

its answer is 5?(3 votes)- Yes, the answer is 5. You can confirm this yourself by substituting 5 into the equation in place of w. Then see if the 2 sides are equal. If they are, then you have a good solution. If the sides are not equal, then you have a math error either in finding the original solution or in your check.(8 votes)

- what if the question was -30= 5(x+1)? How would I solve that?(3 votes)
- -30 = 5(x+1) [We open the bracket]

-30 = 5x+1 [Transposition method]

-30-1 = 5x

Therefore,

-31/5 = x

Have an amazing day, I hope this helped

Thank you!(8 votes)

- Why does it need to be subtracted by 2 and not -16? That's what confuses me :/(3 votes)
- Keep your goal in mind. When you finish solving an equation like the one in the video, your answer needs to look like: X = a number. To accomplish this, you need to isolate X on one side of the equation. This means that anything on the same side as X needs to be moved to the other side. In the video, the 2 is on the same side as X. So, it needs to be moved. If you were to move the 16 instead, then you have everything on the same side as X which doesn't help you achieve your goal.

Hope this helps.(7 votes)

- i still dont understand. can i have some help?(3 votes)
- What part don't you understand?(6 votes)

## Video transcript

We have the equation negative
16 is equal to x over 4, plus 2. And we need to solve for x. So we really just need to
isolate the x variable on one side of this equation, and the
best way to do that is first to isolate it-- isolate this
whole x over 4 term from all of the other terms. So in order
to do that, let's get rid of this 2. And the best way to get rid of
that 2 is to subtract it. But if we want to subtract it
from the right-hand side, we also have to subtract it from
the 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 2
from both sides. So you subtract 2 from the
right, subtract 2 from the left, and we get, on the
left-hand side, negative 16 minus 2 is negative 18. And then that is equal
to x over 4. And then we have positive 2
minus 2, which is just going to be 0, so we don't even
have to write that. I could write just a plus 0,
but I think that's a little unnecessary. And so we have negative 18
is equal to x over 4. And our whole goal here is
to isolate the x, to solve for the x. And the best way we can do
that, if we have x over 4 here, if we multiply that
by 4, we're just going to have an x. So we can multiply that
by 4, but once again, this is an equation. Anything you do to the
right-hand side, you have to do to the left-hand side,
and vice versa. So if we multiply the right-hand
side by 4, we also have to multiply the left-hand
side by 4. So we get 4 times negative 18 is
equal to x over 4, times 4. The x over 4 times 4,
that cancels out. You divide something by 4 and
multiply 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 times
4, 4 times 8 is 32. 4 times 1 is 4, plus 1 is 72. But this is negative 18 times
4, so it's negative 72. So x is equal to negative 72. And if we want to check it, we
can just substitute it back into that original equation. So let's do that. Let's substitute this into
the original equation. So the original equation was
negative 16 is equal to-- instead of writing x, I'm going
to write negative 72-- is equal to negative
72 over 4 plus 2. Let's see if this is
actually true. So this right-hand side
simplifies to negative 72 divided by 4. We already know that that
is negative 18. So this is equal to negative
18 plus 2. This is what the equation
becomes. 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 is
equal to negative 72, does indeed equal negative 16.