Solve for X in the Equation: 5(2-x)+2x=3(4-x)

Let's solve the equation $5(2-x) + 2x = 3(4-x)$ step by step:

First, apply the distributive property to both sides of the equation:

• Left side: $5(2-x) = 5 \cdot 2 - 5 \cdot x = 10 - 5x$.
• Right side: $3(4-x) = 3 \cdot 4 - 3 \cdot x = 12 - 3x$.

Substituting back, the equation becomes:

$10 - 5x + 2x = 12 - 3x$.

Next, combine like terms on the left side:

$10 - 3x = 12 - 3x$.

At this point, notice that the terms involving $x$ on both sides are identical ($-3x$). This means the terms containing $x$ cancel each other out:

$10 = 12$.

Since $10 \neq 12$, we encounter a contradiction.

This implies that there is no solution to the equation. The given equation represents parallel lines that never intersect, so there is no value of $x$ that satisfies the equation.

Therefore, the solution to the problem is There is no solution.