To determine which equation is equivalent to the given equation [tex]\( 2x - 4(2x - 8) = 5x \)[/tex], follow these steps:
1. Start with the original equation:
[tex]\[
2x - 4(2x - 8) = 5x
\][/tex]
2. Simplify the left-hand side by distributing the [tex]\(-4\)[/tex] across the terms within the parentheses:
[tex]\[
2x - 4(2x - 8) = 2x - 4 \cdot 2x + 4 \cdot 8
\][/tex]
Simplify the multiplication inside:
[tex]\[
2x - 8x + 32
\][/tex]
3. Combine like terms on the left-hand side:
[tex]\[
2x - 8x + 32 = -6x + 32
\][/tex]
4. Rewrite the simplified equation:
[tex]\[
-6x + 32 = 5x
\][/tex]
At this point, the simplified version of the given equation is [tex]\(-6x + 32 = 5x\)[/tex].
Let's match this to the provided options:
1. [tex]\( -6x - 8 = 5x \)[/tex]
2. [tex]\( -4x + 32 = 5x \)[/tex]
3. [tex]\( -6x + 32 = 5x \)[/tex]
4. [tex]\( -4x + 16 = 5x \)[/tex]
The equation [tex]\(-6x + 32 = 5x\)[/tex] matches option 3.
Thus, the equivalent equation is:
[tex]\[
\boxed{-6x + 32 = 5x}
\][/tex]
