Evaluate the algebraic expression when x = 4 x=4 x = 4 and y = − 5 y=-5 y = − 5 . 2 y − x ( 3 + y ) 2y-x\left(3+y\right) 2 y − x ( 3 + y )

Alright, folks. So let's get some practice here. So remember what it means to evaluate an algebraic expression, it means that everywhere in this expression that we have, this 2yminusx parenthesis 3+y, I'm gonna replace everywhere that has an x with a 4. So in other words, I'm gonna replace this with a 4. And everywhere I see a y, I'm going to replace it with a negative 5. So that means here and here. Alright? So let's do that first. So what I have here is I have 2, then I have a y, so this this becomes negative 5. And then I have minus this is gonna be x. So remember, my x is supposed to be a 4, I replace it with a 4, and then I have parenthesis 3+andthenyoverhere. So, again, I have to put a negative 5. Now you could put a parenthesis over here. You totally could do that. But because we're just adding and subtracting, you actually don't have to put it there. But I'll just leave it here for now because I'll show you that it doesn't actually do anything. Okay? So okay. So now what we have here is now that we've replaced all of our variables with their given values, now I just have to go through my order of operations. So I have to go through my PEMDAS. And remember, there's a lot of stuff going on in this problem. So we've got multiplication and subtraction, But the first thing we have to do, our first order of business, is always taking care of parentheses. And I see that there is a parenthesis over here that involves 2 things, so I have to deal with that first. Remember, when you see numbers in parentheses sort of next to each other, this just means multiplication. Alright? So I have to deal with this parenthesis first. So what does this 3 and negative five end up becoming? And here, what you can see is that you can actually sort of just drop the parenthesis, and 3 +-five ends up becoming negative 2. Alright? So let me rewrite the expression again. So this is 2 parenthesis negative five minus 4, and now I have parenthesis negative 2. Alright? So now I've dealt with the parenthesis. The next thing I have to do is check for exponents, but there's no exponents, so I could just move on. And now we have to do is before we do any subtraction so remember, there's a subtraction sign here. We actually have to do multiplication and division from left to right. So these two things are multiplied because there's parentheses between them, and these two things are also multiplied. So we just do them from left to right. So this ends up becoming 2 times negative 5, which is negative 10, and then we keep the minus sign, and then the 4 and the negative 2 become negative 8. Alright? So just be really careful with your signs here because you'll see that this 4 and the negative 2 becomes negative 8, but you already had a minus. You already had a subtraction symbol out here, so you can't forget that. And a lot of times, what you'll see when you see 2 negatives is you'll see sometimes a parenthesis that gets stuck in there just to kind of be able to undo this, you know, the, the subtraction symbols. So what they'll do here is they say, well, this is a minus and negative number, so so you can actually sort of just flip the signs and have it become positive, and that's totally fine. Alright? Now the last thing we have to do is just any addition and subtraction. We've taken care of all the multiplication. This isn't really like a parenthesis sign. This is, again, just something we use to sort of visualize the symbols. We do we don't actually have to do anything with this plus 8. Alright? We could just add and subtract. This is -ten plus a plus 8. So remember, this should just be -two. And that is your final answer. So this whole thing, when you evaluate for these given values of x and y, this whole algebraic expression actually just works out to a value of negative 2. All right? So hopefully, you got it. Let me know if you have any questions, and I'll see you in the next video.

0. Fundamental Concepts of Algebra

Algebraic Expressions

Precalculus

0. Fundamental Concepts of Algebra

Algebraic Expressions

Struggling with Precalculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Evaluate the algebraic expression when $x=4$ and $y=-5$ .
$2y-x\left(3+y\right)$

-2

-22

Verified step by step guidance

Identify the given expression: $ 2y - x(3 + y) $.

Substitute the given values into the expression: replace $ x $ with 4 and $ y $ with -5.

The expression becomes: $ 2(-5) - 4(3 + (-5)) $.

Calculate $ 2(-5) $ which is $-10$.

Calculate $ 4(3 + (-5)) $: first find $ 3 + (-5) = -2 $, then multiply by 4 to get $-8$.

5:09m

Watch next

Master Introduction to Algebraic Expressions with a bite sized video explanation from Patrick

Start learning

Algebraic Expressions practice set

Problem sets built by lead tutors

Expert video explanations

Go to Practice

Struggling with Precalculus?

Evaluate the algebraic expression when x=4x=4x=4 and y=−5y=-5y=−5.2y−x(3+y)2y-x\left(3+y\right)2y−x(3+y)

Watch next

Algebraic Expressions practice set

Evaluate the algebraic expression when $x=4$ and $y=-5$ .
$2y-x\left(3+y\right)$