A family is comparing different car seats. One car seat is designed for a child up to and including 2626 lb. Another car seat is designed for a child between 2020 lb and 4040 lb. A third car seat is designed for a child between 2626 lb and 9090 ​lb, inclusive. Model those ranges with compound inequalities. Which car seats are appropriate for a 3030​-lb ​child?

Answer 1

Let's denote the weight of the child as \( x \) in pounds. We can model the weight ranges for each car seat using compound inequalities.

1. First Car Seat: Designed for a child up to and including 2626 lb. \[ x \leq 2626 \]

2. Second Car Seat: Designed for a child between 2020 lb and 4040 lb. \[ 2020 \leq x \leq 4040 \]

3. Third Car Seat: Designed for a child between 2626 lb and 9090 lb, inclusive. \[ 2626 \leq x \leq 9090 \]

Now, let's evaluate which car seats are appropriate for a child weighing 3030 lb.

• For the first car seat: \( 3030 \leq 2626 \) is false, so this car seat is not appropriate.

• For the second car seat: \( 2020 \leq 3030 \leq 4040 \) is true, so this car seat is appropriate.

• For the third car seat: \( 2626 \leq 3030 \leq 9090 \) is true, so this car seat is appropriate.

In summary, the appropriate car seats for a 3030-lb child are the second and third car seats.