Solve the Equation: Determining X in -2(4-3x)+4(2x-4)=8(2-x)

To solve this problem, let's break it down step-by-step:

• Step 1: Expand the equation using the distributive property.

Apply the distributive property to each term: $-2(4 - 3x) + 4(2x - 4) = 8(2 - x)$ $-2 \cdot 4 + (-2) \cdot (-3x) + 4 \cdot 2x - 4 \cdot 4 = 8 \cdot 2 - 8 \cdot x$ which simplifies to:

$-8 + 6x + 8x - 16 = 16 - 8x$

• Step 2: Gather like terms.

Combine $x$ terms and constants separately: $6x + 8x = 14x \quad \text{and} \quad -8 - 16 = -24$ Thus, the equation becomes: $14x - 24 = 16 - 8x$

• Step 3: Isolate $x$ on one side.

Start by adding $8x$ to both sides to bring all terms involving $x$ to one side: $14x + 8x - 24 = 16$ which simplifies to: $22x - 24 = 16$

• Step 4: Solve for $x$.

Add 24 to both sides to isolate the term with $x$: $22x = 16 + 24$ $22x = 40$ Finally, divide both sides by 22: $x = \frac{40}{22} = \frac{20}{11}$

Therefore, the solution to the equation is $\frac{20}{11}$.