Final answer:
A real-world scenario for the equation 5x + 4 = 8x - 8 could be an entrepreneur calculating the break-even point for their business, where 'x' represents the number of goods produced and sold. The equation is solved by isolating 'x', resulting in the need to produce and sell 4 items to cover costs.
Step-by-step explanation:
To create a real-world scenario from the equation 5x + 4 = 8x - 8, imagine you are an entrepreneur starting a business and you are looking at the cost of producing goods versus the revenue from sales. The term 5x could represent the initial investment cost for the production of x number of goods, and the additional 4 dollars could be fixed costs like electricity. On the other side of the equation, 8x could represent the revenue from selling those goods, where each good is sold for 8 dollars, and the term -8 could be discounts or promotional offers that reduce the overall income. To find out how many items need to be produced and sold to break even, you would solve the equation for x.
Solving the equation involves steps like moving all the terms involving x to one side and the constant numbers to the other side:
5x + 4 = 8x - 8
4 + 8 = 8x - 5x
12 = 3x
4 = x
Thus, you need to produce and sell 4 items to break even.