Solving Multi-step Equations - Problem 1
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 very important to distribute the sign of the number as well. If there is a negative number outside of the parenthesis, make sure you are multiplying all the terms inside by a negative number. After the equation has been simplified, then 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 an equation that I know is going to have lots of steps because there is all this stuff that's being done to x. I have to undo it step by step by step. The first thing I'm going to do is to distribute this -2. Be really super careful like I'm going to say this lots of times. It's really important. Be really super careful that not only do you distribute that 2 but you distribute the negative sign also. That -2 gets multiplied by x and the -2 also gets multiplied by 4.
The most common mistake I'll see in a problem like this is that a student would put plus 8 right there instead of a minus 8, be careful to include that minus sign. That 3 I haven't dealt with yet and all of this stuff is equals to 5 still. Okay that was my first step, was distributing the -2.
Next thing I'm going to do is go through and combine like terms. Because I have 3 and -8 I can combine those together as -5 so I'll have -5 take away 2x equals 5. It's kind of confusing some times that when I added together 3 and -8 I didn't do it on both sides of the equation right? I didn't add 8 over on this side to the 5 also. The reason why again is because I'm just combining like terms, I'm ignoring this 5 for now and just simplifying what's on the left side of the equation.
That's another common mistake, is that students forget the difference between simplifying one side of the equation and solving. Like now that I'm ready to solve for x and I say solve because there's no more combining like terms or distributing to do, I'm ready to solve for x now. So this is where you do the same thing to both sides of the equation. I'll have -2x is equal to 10. I'm almost done. To get x by itself I need to divide both sides by -2 so I'll get that x is equal -5. That's my answer I think but I'm going to go back to check it. It's always a good idea when you have these multi-step problems to go back and check.
So let's just double check. Is it true that when I substitute in there -5 for my x value, and then simplify, I'll get 5 as the answer? I sure hope so. Here we go. So when you're doing simplifying you want to be really careful to follow the order of operations and that tells you to do parentheses first. So I'll have, let's see, -5 take away, oh sorry -5 plus 4 is -1, that was my first step. All I did was combine these to get -1.
Next thing I'm going to do in my order of operations is multiply, parentheses mean multiply, so I'll have 3 plus 2 equals 5. Sweet that is a true statement. 5 is equal to 5, that's how I know I did the problem correctly.
Again you guys the most important thing to keep in mind for multi-step problems is the difference between simplifying one side where you're just combining like terms as opposed to where you're solving. And here is where I started solving, where I had to do the same thing to both sides of the equation.