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Video transcript
First, consider the expression for take the quantity of negative 4 times x and add 9. So let's see, we're going to take the quantity of negative 4 times x. Well, negative 4 times x is just going to be negative 4x. And then they say-- so we're going to take that quantity, that's this thing right over here, and then they say add 9. So let's add 9 to it, so that's this first sentence. Take the quantity of negative 4 times x and add 9. That's this expression right over here. Now select the answer that matches the following-- the sum of 4 and the product of negative 9 and that expression. So let's think about this. The sum of 4, so we're going to take 4 and we're going to add it to the product-- we're going to add it to-- I'm running out of colors. Maybe I will do this in this-- let' see. I've already used blue and I've already used orange. I'll use green. So we're going to take that 4, the sum of 4 and the product of negative 9 and that expression. So we're going to add 4 to the product-- we're going to multiply negative 9 times this expression right up here. So it's negative 9 times negative 4x, negative 4x plus 9. Now let's see if any of these actually match what I just wrote right over here. So let's see, this one is 4. Here we're taking a 4 and we're multiplying it times negative 4x minus 9, and then we're subtracting that, so this seems very different, so I'll scratch that one out. Let's see. This has positive 9 times negative 4x plus 9 plus 4, so this is very close, but this says positive 9, this says negative 9, so I'll cross out one out. This one has 4 times 9x plus 4. Well, no, we have negative 4x plus 9, this is different in multiple ways, and they're multiplying it by 4 instead of negative 9. This one, let's see, we have a negative 9 being multiplied by negative 4x plus 9, and then we are adding 4. So all you have to do to go from this expression to this expression, instead of adding the 4 there, you just add the 4 here, and then these two are identical expressions. So we will go with this one right over here.