\[ 1100+600+5 x=700+400+8 x \] (opens in new window) 2 Points \[ \text { boxes } \]

To solve the equation \( 1100 + 600 + 5x = 700 + 400 + 8x \), start by simplifying both sides. You get \( 1700 + 5x = 1100 + 8x \). Next, isolate \( x \) by moving the terms involving \( x \) to one side and the constant terms to the other. Subtract \( 5x \) from both sides: \( 1700 = 1100 + 3x \). Subtract \( 1100 \) from both sides to get \( 600 = 3x \), and finally, divide by \( 3 \) to find \( x = 200 \). So you have 200 boxes! Now, let's think about the significance of equations like this in the real world. These types of linear equations are crucial for budgeting and resource allocation in businesses. For instance, if a company needs to balance costs and profits from boxes produced or sold, using such equations helps determine the optimal quantity for maximum profit. A common mistake when solving equations like this is forgetting to combine like terms properly! Always double-check your arithmetic when simplifying both sides of the equation. Miscalculating a simple addition or subtraction can lead you down the wrong path and give you an incorrect value for \( x \).