\( 5 x \) and \( x+5 \)

Did you know that \( 5x \) and \( x + 5 \) are examples of linear expressions, but they represent different concepts? The first expression, \( 5x \), scales the value of \( x \) by 5, while \( x + 5 \) simply adds 5 to the value of \( x \). When plotted on a graph, \( 5x \) represents a steeper line compared to the gentler slope of \( x + 5 \)! In practical terms, understanding these differences is crucial for real-world scenarios such as budgeting or project planning. If you're managing a business, for instance, \( 5x \) might represent the total revenue from selling \( x \) items priced at $5 each, while \( x + 5 \) could show your projected profits after a fixed overhead cost of $5. Knowing how to manipulate these expressions helps in financial decision-making!