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]
