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## 8th grade foundations (Eureka Math/EngageNY)

### Course: 8th grade foundations (Eureka Math/EngageNY)>Unit 6

Lesson 1: Topic A: Foundations

# 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
• 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
• In this example, why would we divide first then subtract? 30=5(x+1)
• Use the order of operations (or GEMS): Grouping symbols, Exponents, Multiplicatives (Multiplying and dividing), and Subtractives (Subtraction and addition)
• What if there are two variables on one side, ( e.g. -20=-4x-6x)
• 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.
• Anyone knows why we have to subtract on both sides
• 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.
• what if the question was -30= 5(x+1)? How would I solve that?
• -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!
• Can you do a problem that has no fraction
• Why does it need to be subtracted by 2 and not -16? That's what confuses me :/
• 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.