A family is comparing different car seats. One car seat is designed for a child up to and including 3030 lb. Another car seat is designed for a child between 1515 lb and 4040 lb. A third car seat is designed for a child between 3030 lb and 100100 ​lb, inclusive. Model those ranges with compound inequalities. Which car seats are appropriate for a 3838​-lb ​child?

Question

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Part 1
The inequality for a child up to and including 3030 lb is enter your response here

Answer 1

Let's represent the weight ranges of the car seats with compound inequalities.

1. First Car Seat: Designed for a child up to and including 30 lb.

   • Inequality: \( x \leq 30 \)

2. Second Car Seat: Designed for a child between 15 lb and 40 lb.

   • Inequality: \( 15 \leq x \leq 40 \)

3. Third Car Seat: Designed for a child between 30 lb and 100 lb (inclusive).

   • Inequality: \( 30 \leq x \leq 100 \)

Now, let's determine which car seats are appropriate for a 38 lb child:

• First Car Seat: \( x \leq 30 \) → Not Appropriate (38 > 30)
• Second Car Seat: \( 15 \leq x \leq 40 \) → Appropriate (38 falls within the range)
• Third Car Seat: \( 30 \leq x \leq 100 \) → Appropriate (38 falls within the range)

Summary:

• First Car Seat: Not Appropriate for a 38 lb child.
• Second Car Seat: Appropriate for a 38 lb child.
• Third Car Seat: Appropriate for a 38 lb child.