Question

lana works at the front desk at a gym. she is paid $100 a week plus $5 for every new member she enrolls. lana wants her pay to be at least $200 for one week. solve and graph the solution to the inequality for the number of members, m, lana needs to enroll. 100 + 5m ≥ 200

Explanation:

Step1: Subtract 100 from both sides

$$100 + 5m-100\geq200 - 100$$
$$5m\geq100$$

Step2: Divide both sides by 5

$$\frac{5m}{5}\geq\frac{100}{5}$$
$$m\geq20$$

To graph the solution \(m\geq20\) on the number - line:

• Place a closed circle at \(m = 20\) (because the inequality is \(\geq\), so 20 is included in the solution set).
• Draw an arrow to the right of 20 (since \(m\) can be any number greater than or equal to 20).

Answer:

Lana needs to enroll at least 20 members. The graph has a closed circle at 20 and an arrow pointing to the right.