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Solving Equations with a Variable on Both Sides  Problem 1
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
In any single variable equation, start by simplifying  distribute and combine any like terms on both sides of the equation. Now you can start solving using inverse operations. The goal is to get the variable on one side of the equal sign and all the numbers on the other side. Since there are variables on both sides, you want to eliminate the variable from one side of the equation. After you have done this, the variable should only be on one side of the equal sign. Next, you want all the constants on the other side of the equal sign. Use inverse operations to eliminate any constants that are on the same side of the equal sign as the variable. Remember that when solving equations, you must work in the reverse order of PEMDAS.
When you're asked to do homework with solving equations one of the first kind you're going to see is going to look like this and the reason I say this is because there's m's on both sides of the equation. So what I'm going to do is try to simplify as much as I can before I actually solve, simplify meaning combine like terms and distribute and that stuff.
So let's look. This right hand side is already simplified. I can't combine any terms, there's no distributing do that hand side of the equation is ready to go. This side I need to distribute first that 2 gets multiplied by the m and also by the 4 so here we go. 2m take away 8 is equal to 5m plus 7, that's the first step just simplifying the left side. Once I have things simplified I'm ready to solve and solve is like where you do the same thing to both sides of the equation.
There's lots of correct ways to start just keep in mind your goal is to get all of the ms together and all of the regular numbers or constants together. Like for example, this 8 and +7, I want to have them together, I want to have them on the same side of the equals sign. So what I'm going to do is the opposite of taking away 8 is to add 8. I'll add 8 to both sides so that will be 2m, those 8s are gone is equal to 5m plus 15. I'm getting closer because now my mx are spread apart but my constant numbers are combined into 15.
Next thing I'm going t try to do is get these ms together. I want this 5m to be with that 2m so I have to move it. Subtract 5m from both sides and I'll have 3m is equal to 15. Now this is a problem you guys know how to solve. It's like 3 times what number gives you 15. The answer is going to be 5, you can kind of do that in your head. If you're not totally sure just make sure you divide both sides by 3 so that you get m equals 5. That's the final answer.
Most important thing when you see these kinds of problems is to remember that you need to simplify before you start solving, simplify meaning distribute, combine like terms before you start doing this where you're adding numbers to both sides of the equation.
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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Sample Problems (4)
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Solving Equations with a Variable on Both Sides
Problem 1 28,848 viewsSolve for m.
2(m − 4) = 5m + 7 
Solving Equations with a Variable on Both Sides
Problem 2 19,871 viewsSolve for x.
½(x − 8) = 2 − 5 x 2 
Solving Equations with a Variable on Both Sides
Problem 3 13,943 viewsSolve for x.
3(x − 2) + 4 = 2x + 6 + x 
Solving Equations with a Variable on Both Sides
Problem 4 12,675 viewsSolve for x.
2(7x + 3) = 10(x + 1) + 4(x 1)
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