To make a profit, a company’s revenue must be greater than its operating costs. The company’s revenue is modeled by the expression 7.5x – 100, where x represents the number of items sold. The company’s operation costs are modeled by the expression 79.86 + 5.8x. How many items does the company need to sell to make a profit? The inequality that will determine the number of items that need to be sold to make a profit is ? The solution to the inequality is ? The company must sell at least?  items to make a profit.

Answer:106 itemsStep-by-step explanation:We are actually finding the "break even" point, where revenue = costs.Set the revenue 7.5x - 100 equal to the costs 79.86 + 5.8x:7.5x - 100 = 79.86 + 5.8xGroup the x terms together:     1.7x  - 100  =  79.86and then group the constants together on the right side:   1.7x = 179.86Solving for x, we get 105.8 (items)Round this up:  106 itemsThe company will begin making a profit as production passes 106 items.