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## Algebra 1 (Eureka Math/EngageNY)

### Unit 1: Lesson 8

Topic C: Lessons 10-13: Solving Equations- Testing solutions to equations
- Intro to equations
- Testing solutions to equations
- Number of solutions to equations
- Worked example: number of solutions to equations
- Number of solutions to equations
- Creating an equation with no solutions
- Creating an equation with infinitely many solutions
- Number of solutions to equations challenge
- Same thing to both sides of equations
- Representing a relationship with an equation
- Dividing both sides of an equation
- Why we do the same thing to both sides: Variable on both sides

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# Testing solutions to equations

CCSS.Math:

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.