Question

there are many situations that have a minimum or maximum value and many values that will satisfy the situation. consider the following examples. - if each team member needs to sell at least 20 candles for a fundraiser, then a team member who sells 20 candles reaches the goal and a member who sells 24 candles also reaches the goal. any number of candle sales greater than or equal to 20 satisfies the situation. - if the speed limit is 60 mph, then a person driving at a speed of 60 mph is within the speed limit and a person driving 50 mph is within the speed limit. any speed less than or equal to 60 mph satisfies the situation. - in some situations, the value equal to the \boundary number\ does not satisfy the situation and less than or greater than is used without the \or equal to\ component. task: - write a word problem with an unknown value that can be represented by a two - step inequality ((px + q lt r), (px + q gt r), (px + q leq r), or (px + q geq r), where (p), (q), (& r) are rational numbers). - write the inequality to represent the problem. - solve the word problem and explain what the solution means. - graph the solution on a number line.

Explanation:

Step1: Define variable & inequality

Let $x$ = hours worked. Total earnings = hourly pay + bonus, which must be ≥ $230:
$12x + 50 \geq 230$

Step2: Isolate the term with $x$

Subtract 50 from both sides:
$12x + 50 - 50 \geq 230 - 50$
$12x \geq 180$

Step3: Solve for $x$

Divide both sides by 12:
$\frac{12x}{12} \geq \frac{180}{12}$
$x \geq 15$

Step4: Interpret the solution

$x \geq 15$ means working 15 hours or more will earn enough to pay the phone bill. For the number line, a closed circle at 15 includes the value 15, and the right arrow shows all values greater than 15 also satisfy the requirement.

Answer:

1. Word Problem: A part-time job pays $12 per hour, plus a $50 weekly bonus for showing up on time every day. You need to earn at least $230 this week to pay your phone bill. How many hours do you need to work?
2. Inequality: $12x + 50 \geq 230$
3. Solution: You need to work 15 or more hours.
4. Number Line Graph: A closed circle at 15, with an arrow pointing to the right (towards positive infinity).