writing and solving linear inequalities\nto make a profit, a company’s revenue must be greater than its…

writing and solving linear inequalities\nto 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?\nthe inequality that will determine the number of items that need to be sold to make a profit is \nthe solution to the inequality is \nthe company must sell at least items to make a profit.

writing and solving linear inequalities\nto 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?\nthe inequality that will determine the number of items that need to be sold to make a profit is \nthe solution to the inequality is \nthe company must sell at least items to make a profit.

Answer

Explanation:

Step1: Set up the inequality

Since revenue must be greater than operating - costs for profit, we have $7.5x−100>79.86 + 5.8x$.

Step2: Move the $x$ terms to one side

Subtract $5.8x$ from both sides: $7.5x−5.8x−100>79.86+5.8x−5.8x$, which simplifies to $1.7x−100>79.86$.

Step3: Move the constant to the other side

Add 100 to both sides: $1.7x−100 + 100>79.86+100$, resulting in $1.7x>179.86$.

Step4: Solve for $x$

Divide both sides by 1.7: $x>\frac{179.86}{1.7}$. Calculating $\frac{179.86}{1.7}=105.8$.

Answer:

The inequality that will determine the number of items that need to be sold to make a profit is $7.5x−100>79.86 + 5.8x$. The solution to the inequality is $x > 105.8$. The company must sell at least 106 items to make a profit.