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Match the statement with the most appropriate choice from the column on the right.The expressions $3(x-2)$ and $3 x-6$a) Coefficientb) Equivalent expressionsc) Equivalent equationsd) The multiplication principlee) The addition principlef) Solution

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Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 1

Solving Equations

The Language of Algebra

Percent

Equations and Inequalities

Rational Functions

Oregon State University

Harvey Mudd College

Lectures

01:10

Match the statement with t…

01:03

00:45

00:37

Match each expression with…

01:16

Which of the following exp…

00:31

Apply the associative prop…

00:12

Match the property with th…

00:34

00:32

Use the Distributive Prope…

00:33

Use the distributive prope…

00:19

00:18

All right. So if you were given something, like three times the quantity of explosives to and another expression three x 56 and someone asked you what's the best way to describe how they're related? You would say that these two things are what we call equivalent expressions. Okay? And what that means is any two expressions that have the same value. Hey, now you contest out equivalent expressions easily, but is plugging in value for X. So if you're wondering if these two things are the same, you could just plug into value for accents. See this, right? So, for example, X is equal to one, right? Hypothetically, let X equal one. That's testes. See if these two things are equivalent is three. I'm look only of one minus two equivalent to three times one. My assets. Well, three times the quality of one minus two is the same as three times a negative one, which is negative. Three. Is that the same as three minus six. And of course it iss right, So we can see that if you pick any value of X, these two things are gonna be equivalent. Right? So this expression is a good one to this expression. That's what the best relationship is between these two. Now, why are they equivalent? That's because of the distributive property, right? So if you multiply through a summer difference by an outside factor, that's we call the distributive property. So three times a quantity of X minus two is the same as three times the coin may of X plus three times the quantity of negative too. Okay, so when you do that, when you get you get three times X plus negative six, which is exactly the same as three X minus six, so we can see that these two expressions are

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