Simplify −3(5−x)+10−7x-3\left(5-x\right)+10-7x−3(5−x)+10−7x

− 4 x − 5 -4x-5 − 4 x − 5

Simplify − 3 ( 5 − x ) + 10 − 7 x -3\left(5-x\right)+10-7x − 3 ( 5 − x ) + 10 − 7 x

Hi, everyone. Welcome back. Let's get some practice with simplifying algebraic expressions. So we have this expression here, negative 3 into 5 minuteus x plus 10 minus 7 x. Let's get started with the first step here. The first step is we have to distribute, constants and variables into parentheses if you have any, And we clearly do here. We have this negative 3 that's gonna distribute to this 5 and this negative x. So we have to deal with that first before we can start grouping and combining terms. Alright? So let's get started. If we distribute the 3 into the negative 5, this actually just becomes 15, and then the 3 into the negative 3 into the negative x. Just be very careful here because you have a negative that's distributing into another negative, so it actually cancels out the negative. And this ends up becoming plus 3x. Alright? So that becomes those two terms. Okay? And then what happens is we have now the plus 10 minus the 7 x. The first step is done. Now what we have to do is we have to group like terms, and remember, grouping just means that you sort of move the terms around so that the like terms are next to each other. So in other words, we have the 3 x and the negative 7 x that are similar because they both include the variable x. Whereas, these two things are constants, the negative 15 and the 10. They don't have any variables. So let's move these things around so that they're close to each other. Alright? So this actually ends up being I can just start off with the 3 x because it's positive here, so I don't have to worry about a negative sign. So it's positive 3 x. And then when I move this negative 7x over, I have to move the sign with it. So, in other words, I have to move over this negative 7x Because if I had stuck this as a positive, that means that I'm actually adding 7 x in this expression, but I'm not. I'm subtracting it. So I have to keep that sign there. Alright? Just be very careful when you're moving stuff around like this. Okay. So now let's do the constants. Usually, you wanna start off with your positives first because it's just easier. So that's the plus 10, and then we've got the negative 15 that's over here. Remember, you have to move the sign. Alright? So I was going a little slow there because I just wanna make sure that you're grouping these things correctly and you're moving the signs. So that's how you group together the like terms. So now we have the stuff with x's together and the constants together. Now, finally, all we have to do is just combine like terms just by using our rules of operations. Alright? So we have to do 3x minus 7x. This ends up being negative 4x. And then we have the 10 minuteus the 15 and this ends up just being negative 5 So that means our simplified expression ends up just being negative 4x and then minus 5. Alright? So that is our final answer. Notice how, again, it's simpler than the expression that we started out with. We had, you know, these complicated terms with parentheses, but this really just boils down to negative 4 x minus 5. That's it for this one, folks. Hopefully, this made sense.