WEBVTT
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So we have some more chapter 2 problems solving and checking equations.
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So we're on 2.2 part 1, we're on number 9 now.
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So we have 3 times 2x plus 5 equals negative 9.
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The first thing you want to do is simplify each side.
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So I need to do the distributive property here on the left.
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So I have to do 3 times 2x, which is 6x plus 3 times 5, which is 15.
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So I've simplified the left hand side.
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Make sure you don't try to multiply 3 times negative 9, because on the right hand side
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is just the number negative 9.
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Alright, so now we've got the variables and constants on the left and a constant on the right.
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So we want to subtract 15 from both sides of it.
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We only have a 6x on the left hand side of the equation.
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So we have 6x equals.
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And be careful with your positive and negative numbers here.
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Negative 9 plus negative 15 is negative 24.
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Alright, so now we've got 6x equals negative 24.
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We could divide by 6.
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To finally get the answer of negative 4.
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That's the answer, and if it's correct, we could write it as a solution set by putting
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in braces.
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Alright, now we want to check.
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Now when you check you do not do the distributive property.
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You do order of operations.
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There is no need for the distributive property because the distributive property is needed
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when you have variables.
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In the order of operations, you just simplify using the order of operations inside the
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parentheses.
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So inside the parentheses, I have to do 2 times negative 4 first because that's multiplication.
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And I have to still simplify by adding the negative 8 plus 5 in parentheses.
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So I've simplified inside the parentheses.
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All that's left to do is multiply 3 times negative 3, which is negative 9 and the right
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hand side is just negative 9.
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Number 10, we have negative 3x minus 1 third equals 11 thirds.
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You could use the method of multiplying both sides by 3 to eliminate fractions.
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That's one method.
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But in this case, I kind of look ahead and notice if I just add 1 third to both sides,
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I won't even have any fractions anyway.
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So I'm going to go ahead and do that, just realize there's more than one way and usually
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many ways to solve any given equation.
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So we have negative 3x equals, all right, let's do this.
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11 thirds plus 1 third is 12 thirds.
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But 12 thirds is 4.
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So this is really just negative 3x equals 4 when all is said and done.
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So now we have to divide by negative 3 to solve for x so that I get x equals negative 4th
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thirds.
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Don't leave your mind assigned the denominator.
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Just put it out in front or you could put in the numerator.
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So if this is correct, the solution set using braces would be negative 4 thirds.
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All right, let's see if it's correct.
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So we're going to plug in negative 4 thirds for x and there's only one place that there's
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an x, right?
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Now we have to do the order of operations.
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So I multiply the negative 3 times negative 4 thirds.
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And notice the 3's cancel, how very nice and convenient.
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So you could do that, right?
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But then you're going to have to subtract 1 third.
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So you're going to have to go back and get a common denominator.
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So it really doesn't pay to when you multiply cancel the 3's.
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Okay?
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So let's not do that.
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And instead, if you do it, that's all right.
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You'll go back and rewrite it.
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So instead, we're just going to write that as a negative times a negative is 12 thirds
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minus 1 third.
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And now I have a common denominator which is 11 thirds.
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The answer is 11 thirds, 12 thirds minus 1 third.
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And on the right side, there's 11 thirds.
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So if you did write 4 minus 1 third, you could change 4 back to 12 thirds.
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That's one way of doing it.
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And there's other ways to get 11 thirds.
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So that is number 10.
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All right, going on to number 11, we have 7x minus 5 equals 10.
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So we want to isolate the 7x.
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So we add 5 to both sides so that we just get 7x equals 15.
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And divide by 7.
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So x equals 15 seventh.
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All right, well, you know, sometimes your answer is a fraction.
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Fractions are numbers 2, equal opportunity.
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So we happen to have a fraction for an answer.
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That doesn't mean it's wrong.
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A lot of people think that they get a fraction for an answer.
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It's wrong.
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Hmm.
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No reason why it shouldn't be that.
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Now let's check it.
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If you go over here and plug in 15 sevenths for x, I have 15 minus 5.
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See, look at how nice the sevenths cancel.
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Just have 15 minus 5 is 10.
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The check's pretty easy.
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Even though the answer was a fraction, it wasn't so bad to check.
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All right, here's another problem that hounds fractions.
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And again, you could be the problem by multiplying both sides by the least common denominator
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to eliminate fractions.
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But I'm not going to do that because these already have a common denominator.
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So subtracting really isn't so bad.
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We have 2, 11s minus 13, 11s for the coefficients.
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So I know it's going to be negative, and that'll just be a negative 11 over 11 m equals
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3, which is just negative 1.
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So it's really just negative 1m or negative m equals 3.
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And if the opposite of m is 3, then m equals negative 3.
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Remember, you could just take the opposite of both sides or multiply both sides by negative
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1 or divide both sides by negative 1.
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No matter how you do it, you have to end up with m equals negative 3.
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So let's go over here and plug in negative 3.
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So we have 2, 11s times negative 3 minus 13, 11s times negative 3.
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Now when I'm checking, you take the exact problem as it started out and plug in the numbers.
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You don't write that as negative 11, you know, negative 11, 11s, m, et cetera.
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You don't simplify it.
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So what do we have here?
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I need to do both multiplications here.
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So this is negative 6, 11s.
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And here I have minus sign times another minus sign.
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So it's going to be plus and 13 times 3 is 39, 11s.
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And so we have a common denominator of 11s.
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Negative 6 plus 39 is positive 33 and 33 divided by 11 is 3.
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So hit check.
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So doing this problem, you sort of are getting practice with your fractions, aren't you?
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Now, you could do, you know, this problem by multiplying both sides of the equation
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by 11 first.
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And I'm going to go ahead and do that because I have a little room on this video.
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But it's up to you whether or not you do it this way I've shown you or any other number
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of ways.
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As long as you're using properties of equations, you're going to be okay.
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Okay.
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So here's an alternate way.
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If you didn't want to just subtract to begin with, you could go ahead and multiply both
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sides of the equation by 11.
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So I'm just going to do it like this.
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I'm going to multiply each term both sides by 11.
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All right.
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So I want to do 11 times 2, 11's hem minus 11 times 13, 11's hem equals 11 times 3.
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My 11's cancel and my 11's cancel so that I end up with 2m minus 13m equals 33.
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So it's multiplication that I write that as times.
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So I get negative 11m equals 33 divided by both sides by negative 11.
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And once again, you're going to get negative 3, which is what we got doing it the first
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way I did it.
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In case you're interested, I'm going to do the same thing for number 10, which I told you
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the other way you could have done this is multiply both sides of the equation by the least
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common denominator.
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And in this case, the least common denominator would be 3.
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So I multiply by 3 on every term on both sides.
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So we have 3 times negative 3x minus 3 times 1 third equals 3 times 11 thirds.
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So I get negative 9x minus here the 3's cancel.
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So you just have 1.
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And here the 3's cancel so I just get 11.
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So then we would add 1 to both sides and get negative 9x equals 12 divided both sides
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by negative 9 and reduce that.
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So 3 goes into both numbers.
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You get negative 4 thirds.
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It's the same answer we got doing number 10 the other way.
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This was how we did number 10 the first way where we just didn't multiply by the least
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common denominator.
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And we still got x equals negative 4 thirds.
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So a couple different options at least for doing the problems with fractions.