4. What is the solution to the equation \( -0.2(x-20)=44-x \) ? \( \begin{array}{ll}\text { (A) } x=-90 & \text { (C) } x=50 \\ \text { (B) } x=-50 & \text { (D) } x=90\end{array} \)

To solve the equation \( -0.2(x-20)=44-x \), we first distribute the left side: \[ -0.2x + 4 = 44 - x \] Next, we can isolate \( x \) by bringing all terms involving \( x \) to one side of the equation and the constants to the other side: \[ -x + 0.2x = 44 - 4 \] This simplifies to: \[ -0.8x = 40 \] Now we can divide both sides by -0.8: \[ x = \frac{40}{-0.8} = -50 \] So, the solution is \( x = -50 \), which corresponds to option (B). Here’s a fun fact: solving algebraic equations like this one is essential in various fields, from engineering to economics, helping professionals optimize systems and financial models! When working with equations, a common mistake can be misapplying the distributive property or dropping negative signs. Always double-check your work to ensure you haven’t accidentally altered the signs of any terms during the solution process!