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Solving Single-step Equations - Problem 2
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. For example, if the variable is being multiplied by 3, then to isolate the variable, do the opposite operation, which is dividing by 3. If one side is divided by 3 to isolate the variable, then the other side must be divided by 3 as well. After solving for the variable, check your answer by plugging the value into the original equation. If the equation is true -- meaning the left side of the equation equals the right side of the equation -- then the solution is correct.
We're continuing working on solving equations and the important thing to keep in mind is that whatever you do to one side of the equation, you have to do to the other side also. I want to kind of undo whatever's been done to x, that's in general what I'm going to try to do.
So what this problem means if I were to turn this into a sentence, it would mean 3 times a number equals 17. Hang on a second, 3 times nothing is 17 right? Like 3 times 5 is 15, 3 times 6 is 18, nothing is 17. Except for my friends we might get a fraction sometimes and that might freak you out but I promise it will be okay. Let me show you how this works.
This means 3 times x, right? And in order to solve an equation I want to do the opposite of timesing which is dividing. So if I divide both sides by 3 like this, then what you know about fractions is that 3/3 kind of cancels out. It's like a giant 1 right there, 3/3 as a fraction is like the number 1, so what I really have is that x equals 17/3. That's my fractional answer. Don't freak out like 17/3 is a weird number we probably don't see that very often but it can still work. It can still be the solution to this equation.
And just so you guys believe me let's do a quick check on my paper I would write like, hey teacher here's where I'm checking my solution and I would say 3 times, this is where I'm going to use my new number, 17/3, I hope is equal to 17, and then to make sure this is true think about what you know about multiplying fractions. If I turn this into 3/1 then I can see that my 3s would cancel out just like that same giant 1 situation and I'd be left with 17 equals 17, sweet!
So what I want to show you guys today is like you don't always get a whole number, you don't always get x equals 5, x equals 10, sometimes you get x equals 17/3. Don't freak out, it still works.