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 multi-step equations, start by simplifying both sides of the equations, as needed. This means to get rid of any parenthesis by distributing, combine any like terms, and so forth. When using the distributive property, it is important to distribute the sign of the number as well. After distributing, combine like terms. Once the equation has been simplified, use inverse operations to solve for the unknown variable. Remember that solving an equation and finding the value of the variable requires "undoing" what has been done to the variable. Since an equation is two expressions that are equal to each other, this means that 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 multi-step equation, work in the reverse order of PEMDAS.
This is the kind of problem that I know is going to involve multiple steps because there's lots of things that are going on with x. Not only that but there's two x chunks so I know I'm going to have to add those together or combine like terms at some point. First thing I'm going to do is distribute this 3 so that I'll have 5x plus 3x and then 3 times -4 is -12. Be really careful with that negative sign. No I'm ready to combine like terms where I'm going to add 5x plus 3x together that's 8x.
Now I'm done simplifying the left side. Everything I've done so far is just trying to simplify that piece only. Everything I've done is like just trying to get the Xs together, get my regular constant numbers together, it's all just simplifying.
Now I'm ready to solve the equation and the way I know is because I have only one x term and only one regular number or constant term on the left side. There's no more combining like terms to do. So to solve I'm going to do the same thing to both sides of the equation, 8x is equal to 28. Last but not least I don't want what 8x is, I want what regular old x is. That's how I know I need to do the opposite of multiplying which is to divide both sides by 8, so I'll have x is equal 28/8. If you want to reduce that fraction which is the most proper form for Math answers, you would have to go through and divide 28/8 by the same number.
So let's see, what goes into 8 and 28? 4 I think is the biggest number so if I divide the top and bottom by 4, I'll have x is equal to 7/2 or you could write that as 3 ½, either way is fine.
Again the most important thing to keep in mind is the difference between simplifying one side of the equation which is all this distributing, combining like terms business, before you come into solving and that's where you do the same thing to both sides.
