Simplify 3 x + 14 y − 7 ( − x + 2 y ) 3x+14y-7\left(-x+2y\right) 3 x + 14 y − 7 ( − x + 2 y )

Welcome back, everyone. Let's check out this practice problem. So we have 3x+14y, then we've got minus 7 that gets multiplied into negative x plus 2y. Alright? We have to simplify this expression. First thing we have to do, distribute any constants or variables into parentheses. So let's take a look at this -seven into this -x plus 2y. If you multiply -seven into -x, remember, the negatives cancel, and you end up with 7x that is a positive. Then if you multiply the negative x into the 2y, you have to multiply. So that means that ends up being negative 14 y. So you end up with one negative sign. And then we're just going to repeat all this stuff over here. So this is going to be 14 y, and then we have a plus and then a 3x. Alright? Notice how I have 2 different kinds of terms in this problem. I actually have no constants, but I do have stuff with x's, like 3x and 7x, and I do have stuff with y's, like 14, and negative 14y. That brings us to the next step. We're gonna have to group together like terms. So just me we're gonna move them to the they're next to each other. So this ends up being 3x+7x. Notice how the x terms are together now, and I've brought over their respective signs. And then I have a 14 y that's positive. So I keep that sign over here, And then I have a negative 14 y. Again, I'm keeping the sign of that negative 14 as I move it over. You basically just wanna make sure that you end up with all the same signs that you started off with. Alright? So now the last thing is just to go ahead and combine those like terms. 37 just become 10 x, and then I have 14, positive 14, and negative 14. This actually would just end up cancelling out to 0. If I have 14 to something and then I take 14 away, I end up with nothing. So this actually, the whole thing ends up just being 10 x. And that is your final answer. Alright, folks. So pretty straightforward. Let me know if you have any questions.

Simplify 3 x + 14 y − 7 ( − x + 2 y ) 3x+14y-7\left(-x+2y\right) 3 x + 14 y − 7 ( − x + 2 y )

10 x + 16 y 10x+16y 10 x + 16 y

17 x − 7 y 17x-7y 17 x − 7 y

0. Fundamental Concepts of Algebra

Algebraic Expressions

Precalculus

0. Fundamental Concepts of Algebra

Algebraic Expressions

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Multiple Choice

Simplify
$3x+14y-7\left(-x+2y\right)$

$10x$

$10x+16y$

$10y$

$17x-7y$

Verified step by step guidance

Start by distributing the -7 across the terms inside the parentheses: -7(-x + 2y). This means you will multiply -7 by each term inside the parentheses.

Calculate the distribution: -7 * (-x) = 7x and -7 * 2y = -14y. So, the expression -7(-x + 2y) simplifies to 7x - 14y.

Substitute the simplified expression back into the original equation: 3x + 14y + (7x - 14y).

Combine like terms: Add the x terms together (3x + 7x) and the y terms together (14y - 14y).

Simplify the expression: 3x + 7x = 10x and 14y - 14y = 0. Therefore, the simplified expression is 10x.

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Simplify3x+14y−7(−x+2y)3x+14y-7\left(-x+2y\right)3x+14y−7(−x+2y)

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Simplify
$3x+14y-7\left(-x+2y\right)$