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## Operations and Algebraic Thinking 218-221

### Course: Operations and Algebraic Thinking 218-221>Unit 5

Lesson 1: Algebraic equations basics

# Testing solutions to equations

A solution to an equation makes that equation true. Learn how to test if a certain value of a variable makes an equation true.

## Video transcript

- [Voiceover] So we've got an equation here, it says five times x minus three is equal to four times x plus three. So, what we want to do is we want to figure out an x that satisfies this, so there's some number that if I take five, multiply it by that number, subtract three from it, that's going to be the same thing as if I take four times that number and add three to it. And, before we go into how to solve these types of things, let's just first see if we can test whether something does satisfy this equation. And so, I have three options here, I have x could be equal to five, x could be equal to six, and x could be equal to seven. And your goal is to pause this video and figure out which of these x's satisfies this equation, which of these values would make this equation be true. So, I'm assuming that you have tried that, so let's work through each of them, step one by one. So let's see this first one: if x is equal to five, then in order for this to be true, five time five, right, five times x, so five times five minus three needs to be equal to four times, everywhere we see an x we're going to put a five there, four times, actually let me do it this way. Let me just color code it. So this is the same thing as saying five times five minus three, let me do that in that same color, minus three, needs to be equal to four times five, four times five plus three, plus three. Color changing is hard. Plus three. Now, is this true? Let's see, five times five is 25, it's going to be 25 minus three, needs to be equal to 20 plus three. 25 minus three is 22, needs to be equal to 23. No, this is not true. So, x does not equal five, so this is not a solution. Let's try x equals six. So, once again, we're going to do five times our x, which is going to be six, actually let me just write it out, minus three needs to be equal to four times our x, plus three, and in this case our x is six, so it's going to be five times six minus three needs to be equal to four times six plus three. What's five times six? Well, it's 30 minus three, needs to be equal to four times six is 24, and then plus three. Well, this is true, 30 minus three is 27, which is indeed equal to 24 plus 3, it's equal to 27. So x equals 6 does satisfy our equation, it is a solution, and actually as we'll see in the future, the solution to this equation right over here. X equals six satisfies this. Now, just for good measure, let's just varify that x equals seven will not satisfy. So I'm going to move this up a little bit. So if x is equal to seven, we're going to get five times seven minus three needs to be equal to four time seven plus three. And so, we're going to get, and in all these cases we do the multiplication first, order of operations, and it's very clear when you see it kind of in the algebraic notation up here, so we're going to do 35 minus three needs to be equal to 28 plus three, 35 minus three is 32, 28 plus three is 31, these do not equal each other. So this is not a solution to our original equation.