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Solving Two-step Equations - Problem 1 24,773 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 2m + 3 = -11, the variable is being multiplied by 2 then added by 3. To solve for the variable, start by subtracting 3 from both sides, then divide both sides by 2. Don't forget to check your answer by plugging in the value of the variable into the original equation.

In order to solve an equation like this it's going to involve a couple different steps and the way I can tell is because not only is m being multiplied by 2 but there's also this +3 business that I have to deal with. So when you get an equation like this we're going to have to do more than one step. Keep in mind whatever you do to one side of the equation, you need to do the exact same thing to the other side.

So the first thing I want to do to get m all by itself would be to subtract 3 from both sides because I'm undoing that +3 right there. So now I would have 2m equals -14 and now you can probably do this is your brain, 2 times what number gives you the answer -14? Well it's -7. The official Math way to do it would be to divide both sides by 2. Those cancel out and I'm left with m equals -14/2 which is the same as -7.

So it's important that whatever you do to this side of the equation, this expression, you do the exact same thing to this expression all the way around. Don't forget to check your answer. I think my answer is going to be m equals -7 but to double check, 2 times -7 plus 3, I hope is equal to -11 and the way I'll be able to tell is by doing this out and using the order of operations to simplify it. -14 plus 3 is equal to -11, I did the multiplying part first because of PEMDAS, Parentheses, Exponents, Multiply, Divide, Addition, Subtraction and it's true that -14 plus 3 is equal to -11. That's how I know I got the right answer.

So again the last thing to keep in mind when you have problems like this where you're going to have lots of different steps going on is that you do the exact same thing to both expressions or to both sides of the equal sign.

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