WEBVTT

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Welcome to Brainfuse!

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In this lesson, we'll use our understanding of the operations to write expressions and equations.

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This is especially helpful when you need to solve application problems.

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Here are the instructions on screen.

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Let x denote a number and express the following statements algebraically:

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These instructions are asking us to use x as our variable.

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Let's start with the first statement, "The sum of a number and 3."

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This is an example of an algebraic expression.

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These are statements with at least one variable,

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here we have "a number,"

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Which we'll represent with an x,

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And at least one operation. Here we have the keyword "sum,"

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Which tells us that we're going to be adding two or more values together.

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So, "sum of a number and 3,"

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It's "x + 3," and because this is addition,

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We can also write that in the opposite order and have the same sum.

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That's one property of addition.

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Let's move to the next expression.

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Here we have "4 more than a number,"

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And our key word, "more," also calls for adding values.

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So we can write this as "x + 4,"

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Or "4 + x."

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Both would have the same sum.

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So as we saw with these examples in red, order does not matter with addition.

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But next, let's look at the orange expressions.

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The first one says, "the difference between 3 and x."

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We tend to express the difference between two numbers

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As a positive value.

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If we had to express the difference between

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5 and 3,

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For example,

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The lesser value, 3, needs to be subtracted from the greater value.

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So 5 - 3 would equal positive 2.

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That would be the difference.

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But here,

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We have a problem.

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This says, "the difference between 3 and x,"

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And

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We don't know whether x is greater than, equal to, or less than 3.

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So if you don't know which value is greater, you can use absolute value.

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So in that case we can write 3 - x

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Between the absolute value bars,

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Or x - 3.

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Using absolute value ensures that our answer will be positive and these two values will be equal.

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After all, if x were equal to 5, then the absolute value of 3 - 5

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Would be equal to the absolute value of -2.

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Or, if we had 5 - 3, the absolute value of 5 - 3

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That would be equal to the absolute value of 2.

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Both of these are equal to positive 2.

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For our next expression, we have "2 less than a number."

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"Difference" was a term that calls for subtraction, and "less than" in this case is the term that calls for subtraction.

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In this case, check to make sure you have the right order.

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I'm going to write down

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Two different possible answers

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And then we can figure out which one is correct.

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So, this one is saying that we start with 2 and we subtract

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An unknown value from it.

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This one is saying that we start with a number

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And we subtract 2 from it.

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So "x - 2" has the same meaning as "2 less than a number."

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We start with a number, and our result is 2 less than that number.

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So let's cross out the wrong answer and keep the correct one.

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Okay, so stepping down to the green expressions,

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Here we have, "the product of a number and 4."

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"Product" calls for multiplication,

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We can write that as 4 times x, or 4x.

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You'll often see in these expressions.

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And "twice a number." "Twice" is another way of saying 2 times,

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So we can write that

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As 2 times x, or 2x.

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And now here we have a percentage.

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So "30% of a number."

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"Of" tells us to multiply, but we need to remember that we have a percent.

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So let's convert that percentage into a fraction or decimal.

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There it is as a fraction, 30% = 30 for every 100,

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Or 30 over 100.

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And to convert it to a decimal,

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We divide by 100 by drawing the decimal point back two places.

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So we end up with

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0.30 times a number, or 0.30x.

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And in the blue statement we have, "the quotient of 8 and a number," and "quotient" tells us to divide.

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So here, order does matter.

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And it gives us the dividend first, the 8,

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Divided by

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The divisor, which is our number.

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It can also be written

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Like that,

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And our answer would be the quotient.

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So far we have only had one operation per problem.

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But in these last two problems, we're going to have more than one.

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Here we have "twice the sum of 8 and a number," so this calls for

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2 times, that's multiplication, the sum of 8 and a number, that's addition.

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When we write this out,

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We need to use parentheses, because before we multiply we need to find the

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Sum of 8 and a number.

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So inside the parentheses you can put "8 + x" or "x + 8,"

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And

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Then we want to multiply that sum by 2.

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So in this case we use grouping symbols, or parentheses,

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To show that this sum needs to be found first,

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Before multiplying.

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And as I read the final statement notice what makes it different from the others.

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"12 less than 3 times a number is equal to 8 more than 2 times the quotient of that number and 4."

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Number 1, it's extremely long, but it also has

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A key word in it that makes this an equation,

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Not an expression. And that is "equal."

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You may see "is equal," "equals,"

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"Is equivalent to," (etc.) These terms

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Tell us that

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We're working with an equation.

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An equation shows what makes one value equal to another.

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Let's start on the left side of the equal sign.

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Here we have

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"12 less

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Than 3 times a number,"

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So we'll first multiply 3 times a number

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And subtract 12

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From that product.

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Then we have "is equal."

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So we can add the equal sign, and now

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Let's work with the right side of the equation.

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Here we have "8 more

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Than 2 times

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The quotient

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Of that number and 4." So that's division.

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So in parentheses, first we would need to find

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The quotient of that number and 4

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And then this problem tells us to multiply

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That quotient by 2

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And

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This value would then be 8 more

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Than the product of 2 times x/4,

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So we need to add 8 to it.

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Since this is an equation, we can actually solve for x, so let's go ahead and do that.

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I'll need to scroll down a bit, so I hope this doesn't make you seasick.

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If so, look away from the screen.

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Now we have

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3x - 12

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Equals, let's multiply 2 times x/4,

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So that's 2x over 4, plus 8.

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So to get rid of the denominator, let's multiply both sides by 4.

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On this side, that gives us 12x - 48

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And that's set equal to

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4 times 2x/4 is equal to 2x, because the 4's cancel out,

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Plus, 4 x 8 is 32.

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Now let's isolate the x

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By subtracting 2x

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From both sides.

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That leaves us with 10x - 48

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Equals 32.

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And let's add

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48 to both sides.

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Scroll up a little bit more,

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And that is 10x

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Equals

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8 + 2 is 10, carry the 1, and 4 + 3 + 1 is 8,

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So we divide both sides by 10 to isolate that x,

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And 80 divided by 10 equals 8.

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So we were able to write expressions in this lesson,

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And an equation that we solved.

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Scroll back up, and we can end it here.

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Now it's your turn to practice using this skill, and remember to pay attention to the operation you're using.  Ask yourself if order matters. Thanks.