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Solving Two-step Equations - Problem 2 14,909 views

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

Two-step equations means that two steps need to be taken in order to solve the equation. Solving an equation and finding the value of the variable requires "undoing" what has been done to the variable. We do this by using inverse operations to isolate the variable. Remember that an equation is two expressions that are equal to each other. This means that when using inverse operations to isolate the variable, what is done to one side of the equation has to be done to the other side as well so that the equation stays balanced. In a two-step equation, work in the reverse order of PEMDAS. For example, in the equation k/3 + 7 = -20, the variable is being divided by 3 then added by 7. To solve for the variable, start by subtracting 7 from both sides, then multiplying both sides by 3. Don't forget to check your answer by plugging in the value of the variable into the original equation.

When I look at this problem I know I'm going to have to do a couple of different steps because k is being divided by 3 and then that quotient has a +7 after it so I'm going to have to undo all of that business in order to figure out what my k value is.

So the first thing I want to do is undo that +7 by subtracting 7 from both sides so I'll get k/3 equals -27. A lot of students stop right here and they think okay k equals -9. Please don't say k equals -9 because -9/3 is not -27. Don't be too hard on yourself if you do say this though because what's happening in your brain is you're saying okay 3 and -27 there's a -9 involved somewhere in there and you're just guessing that's the answer. You have to be really careful with that, Math teachers love that kind of trick.

The proper way to solve this problem is to multiply both sides by 3 and the way I know that is because right now k is being divided by 3 and the opposite of dividing by 3 is to multiply by 3. So I'm going to go through and multiply both sides by 3 so now those 3s cancel out and I'd be left with k equals -27 times 3 is -81. That's how you can find the correct answer.

Be really careful when you get to the end that you don't let your brain take over on autopilot and write down something like -9. So be sure to keep in mind when you have problems like this with multiple steps again you have to do the same thing to both sides of the equation. Subtract 7 so that k/3 is isolated and then multiply both sides by 3.