A family is comparing different car seats. One car seat is designed for a child up to and including 30 lb. Another car seat is designed for a child between 15 lb and 40 lb. A third car seat is designed for a child between 30 lb and 100 ​lb, inclusive. Model those ranges with compound inequalities. Which car seats are appropriate for a 38-lb ​child?

Question

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Part 1
The inequality for a child up to and including 30 lb is enter your response here

Answer 1

To model the weight ranges of the car seats with compound inequalities, we have the following:

1. For the car seat designed for a child up to and including 30 lb:

   • The inequality is: \[ x \leq 30 \] where \( x \) represents the weight of the child.

2. For the car seat designed for a child between 15 lb and 40 lb:

   • The inequality is: \[ 15 < x < 40 \]

3. For the car seat designed for a child between 30 lb and 100 lb, inclusive:

   • The inequality is: \[ 30 \leq x \leq 100 \]

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

1. Car seat 1 (up to and including 30 lb):

   • The child does not fit this car seat because \( 38 > 30 \).

2. Car seat 2 (between 15 lb and 40 lb):

   • The child fits this car seat because \( 15 < 38 < 40 \).

3. Car seat 3 (between 30 lb and 100 lb, inclusive):

   • The child fits this car seat because \( 30 \leq 38 \leq 100 \).

Conclusion:

A 38-lb child is appropriate for car seat 2 and car seat 3.