To determine which expression is equivalent to [tex]\(4x + 6y - 8x\)[/tex], follow these steps:
1. Simplify the given expression:
[tex]\[
4x + 6y - 8x
\][/tex]
Combine the like terms involving [tex]\(x\)[/tex]:
[tex]\[
4x - 8x + 6y = -4x + 6y
\][/tex]
The simplified expression is:
[tex]\[
-4x + 6y
\][/tex]
2. Analyze each option provided to find the equivalent expression:
Option A: [tex]\(2(3y - 2x)\)[/tex]
[tex]\[
2(3y - 2x) = 2 \cdot 3y - 2 \cdot 2x = 6y - 4x
\][/tex]
This simplifies to:
[tex]\[
-4x + 6y
\][/tex]
Option A is equivalent to the simplified expression [tex]\(-4x + 6y\)[/tex].
Option B: [tex]\(2(4y - 2x)\)[/tex]
[tex]\[
2(4y - 2x) = 2 \cdot 4y - 2 \cdot 2x = 8y - 4x
\][/tex]
This simplifies to:
[tex]\[
-4x + 8y
\][/tex]
Option B is not equivalent to [tex]\(-4x + 6y\)[/tex].
Option C: [tex]\(2(2x + 3y)\)[/tex]
[tex]\[
2(2x + 3y) = 2 \cdot 2x + 2 \cdot 3y = 4x + 6y
\][/tex]
This simplifies to:
[tex]\[
4x + 6y
\][/tex]
Option C is not equivalent to [tex]\(-4x + 6y\)[/tex].
Option D: [tex]\(2(3x - 2y)\)[/tex]
[tex]\[
2(3x - 2y) = 2 \cdot 3x - 2 \cdot 2y = 6x - 4y
\][/tex]
This simplifies to:
[tex]\[
6x - 4y
\][/tex]
Option D is not equivalent to [tex]\(-4x + 6y\)[/tex].
Therefore, the expression that is equivalent to [tex]\(4x + 6y - 8x\)[/tex] is Option A: [tex]\(2(3y - 2x)\)[/tex].
