Solve the Equation: Simplifying -8(4-x) + 4(2x+5) = 2(7-2x)

To solve this linear equation, we will proceed step by step:

• Step 1: Apply the distributive property to both sides of the given equation.
• Step 2: Combine like terms on both sides.
• Step 3: Rearrange the equation to isolate the variable $x$.
• Step 4: Solve for $x$ and verify against the choices provided.

Now, let's work through each step:

Step 1: Apply the distributive property:
$-8(4 - x)$ becomes $-32 + 8x$ and $4(2x + 5)$ becomes $8x + 20$.
The right side $2(7 - 2x)$ becomes $14 - 4x$.

This gives us the new equation:
$-32 + 8x + 8x + 20 = 14 - 4x$.

Step 2: Combine like terms:
On the left side: $-32 + 20 + 8x + 8x = -12 + 16x$.
On the right side: $14 - 4x$ remains unchanged.

The equation simplifies to:
$-12 + 16x = 14 - 4x$.

Step 3: Rearrange the equation to isolate $x$.
Add $4x$ to both sides to move the $x$ terms to one side:
$-12 + 16x + 4x = 14$.
This simplifies to:
$-12 + 20x = 14$.

Next, add 12 to both sides to isolate terms with $x$:
$20x = 14 + 12$.
Thus, $20x = 26$.

Step 4: Solve for $x$:
Divide by 20:
$x = \frac{26}{20} = \frac{13}{10}$.

Therefore, the correct solution is $x = \frac{13}{10}$, which corresponds to choice 3.