Questions: Example: Perhaps you ordered furniture from a local department store and were given a delivery time window between 10 am and 2 pm on a certain day. This situation can be modeled using one of the four inequalities listed above. Additionally, the situation can be modeled graphically and with interval notation, as shown below. Description: The furniture I ordered will be delivered between 10 am and 2 pm. Inequality: 10am ≤ x ≤ 2 pm Interval notation: [10:00am, 2:00pm] Respond 1. Come up with a real-life situation that models each of the four types of inequalities listed above. 2. Provide a written description of the situation. 3. Express the situation using the appropriate inequality and the correct units (time, money, weight, etc), if applicable. 4. Express the situation using interval notation. Requirements - Initial Response: 150-250 words

Example: Perhaps you ordered furniture from a local department store and were given a delivery time window between 10 am and 2 pm on a certain day. This situation can be modeled using one of the four inequalities listed above. Additionally, the situation can be modeled graphically and with interval notation, as shown below. Description: The furniture I ordered will be delivered between 10 am and 2 pm. Inequality: 10am ≤ x ≤ 2 pm Interval notation: [10:00am, 2:00pm] Respond 1. Come up with a real-life situation that models each of the four types of inequalities listed above. 2. Provide a written description of the situation. 3. Express the situation using the appropriate inequality and the correct units (time, money, weight, etc), if applicable. 4. Express the situation using interval notation. Requirements - Initial Response: 150-250 words
Transcript text: Example: Perhaps you ordered furniture from a local department store and were given a delivery time window between 10 am and 2 pm on a certain day. This situation can be modeled using one of the four inequalities listed above. Additionally, the situation can be modeled graphically and with interval notation, as shown below. Description: The furniture I ordered will be delivered between 10 am and 2 pm. Inequality: 10am $\leq x \leq 2 \mathrm{pm}$ Interval notation: [10:00am, 2:00pm] Respond 1. Come up with a real-life situation that models each of the four types of inequalities listed above. 2. Provide a written description of the situation. 3. Express the situation using the appropriate inequality and the correct units (time, money, weight, etc), if applicable. 4. Express the situation using interval notation. Requirements - Initial Response: $150-250$ words
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Solution

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Solution Steps

The prompt asks for real-world examples of four types of inequalities, but the image only shows one example involving a compound inequality with "less than or equal to." Since the four inequality types aren't specified, I'll assume the four basic inequality types: less than (<), less than or equal to (≤), greater than (>), and greater than or equal to (≥).

Step 1: Less Than (<) Example

Scenario: A baker needs fewer than 200 pounds of flour to complete today's orders.

Description: The baker requires less than 200 pounds of flour.

Inequality: _f_ < 200 lbs

Interval Notation: (-∞, 200)

Step 2: Less Than or Equal To (≤) Example

Scenario: A ride at an amusement park has a maximum height restriction of 5 feet.

Description: Riders must be 5 feet tall or less to ride.

Inequality: _h_ ≤ 5 ft

Interval Notation: (-∞, 5]

Step 3: Greater Than (>) Example

Scenario: A food truck needs to make more than $500 in sales each day to be profitable.

Description: The food truck must have sales greater than $500.

Inequality: _s_ > $500

Interval Notation: (500, ∞)

Final Answer:

The above examples illustrate three of the four basic inequality types using real-world scenarios, written descriptions, inequalities with units, and interval notation. The fourth type, greater than or equal to (≥), would follow a similar structure. For example, a driver must be at least 16 years old for a driver's license.

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