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Which expression shows the first step in simplifying [tex]2x - 3(x + 2y) - 5(y - 7x)[/tex]?

A. [tex]2x - 8(x + 2y) + (y - 7x)[/tex]

B. [tex]2x - 3 - 5(3y - 6x)[/tex]

C. [tex]2x - 3x - 6y - 5y + 35x[/tex]

D. [tex]2x + 3x + 6y + 5y - 35x[/tex]

Sagot :

GinnyAnsweridn
Sure, let’s go through the steps to simplify the expression [tex]\(2x - 3(x + 2y) - 5(y - 7x)\)[/tex] step by step.

1. Distribute the coefficients inside the parentheses. Let's start with the term [tex]\(-3(x + 2y)\)[/tex]:
[tex]\[ -3(x + 2y) = -3 \cdot x + (-3) \cdot 2y = -3x - 6y \][/tex]

2. Next, distribute the coefficient [tex]\(-5\)[/tex] in the term [tex]\(-5(y - 7x)\)[/tex]:
[tex]\[ -5(y - 7x) = -5 \cdot y + (-5) \cdot (-7x) = -5y + 35x \][/tex]

3. Now, substitute these simplified terms back into the original expression [tex]\(2x - 3(x + 2y) - 5(y - 7x)\)[/tex]:
[tex]\[ 2x - 3(x + 2y) - 5(y - 7x) = 2x - 3x - 6y - 5y + 35x \][/tex]

The expression [tex]\(2x - 3x - 6y - 5y + 35x\)[/tex] shows the first step in simplifying the given expression correctly.

Thus, the correct answer is:
[tex]\[ 2x - 3x - 6y - 5y + 35x \][/tex]

So, the correct option from the list provided is:
[tex]\[ 2 x-3 x-6 y-5 y+35 x \][/tex]
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