Question

writing and solving linear inequalities

to make a profit, a companys revenue must be greater than its operating costs. the companys revenue is modeled by the expression (7.5x - 100), where (x) represents the number of items sold. the companys 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 dropdown

the solution to the inequality is dropdown.

the company must sell at least dropdown items to make a profit.

dropdown options:
(7.5x - 100 > 79.86 + 5.8x)
(7.5x - 100 < 79.86 + 5.8x)
(7.5 - 100x > 79.86x + 5.8)
(7.5 - 100x < 79.86x + 5.8)

Explanation:

Set up the inequality

Using the Solving Linear Inequalities knowledge point

$$
LATEXBLOCK0
$$

Solve for x

Using the Solving Linear Inequalities knowledge point

$$
LATEXBLOCK1
$$

Express in interval notation

Using the Interval Notation knowledge point

$$ x \in (105.8, \infty) $$

Determine the minimum items

Since the number of items sold \(x\) must be a whole number:

$$
LATEXBLOCK2
$$

Answer:

Question 1

The inequality that will determine the number of items that need to be sold to make a profit is <blank>\(7.5x - 100 > 79.86 + 5.8x\)</blank>

Question 2

The solution to the inequality is <blank>\(x > 105.8\)</blank>

Question 3

The company must sell at least <blank>106</blank> items to make a profit.