Simplify the expression $5 x + 4 y - 3 x - 7 y + 8 x$ by collecting the like terms together.

2 x + 3 y

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2 x - 3 y

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10 x + 3 y

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10 x - 3 y

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Solution

The correct option is D $10 x - 3 y$
We are given with an expression: $5 x + 4 y - 3 x - 7 y + 8 x$

The like terms involving the variable $x$ are: $5 x, - 3 x,$ and $8 x$

The like terms involving the variable $y$ are: $4 y$ and $- 7 y$

Adding the like terms involving the variable $x$ :
$5 x - 3 x - ------- - + 8 x = 2 x + 8 x$

$2 x + 8 x - ------- - = 10 x$

$∴ 5 x - 3 x + 8 x = 10 x$

Adding the like terms involving the variable $y$ :
$4 y - 7 y - ------ - = - 3 y$

Simplification of the given expression would be obtained by adding the like terms involving $x$ and $y$ .
This can be shown as:

$5 x + 4 y - 3 x - 7 y + 8 x$

$= 5 x - 3 x + 8 x - ------------ - + 4 y - 7 y - ------ -$

$= 10 x - 3 y$

$∴ 5 x + 4 y - 3 x - 7 y + 8 x = 10 x - 3 y$

As a result, the expression $5 x + 4 y - 3 x - 7 y + 8 x$ after simplification would become $10 x - 3 y$ .

Therefore, option (d.) is the correct answer.

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