### Video Transcript

A state’s regulations to ensure
child passenger safety are as follows. From the age of 18, there is no
legal requirement for passengers traveling in the backseat of a car to use a seat
belt. Children under one year of age and
children weighing less than 20 pounds are required to be in a rear-facing seat. Children age one to age three
years, inclusive, and at least 20 pounds in weight are required to be in a
forward-facing seat. Children age four to age seven
years, inclusive, are required to be in a forward-facing car seat or a booster
seat. Children at eight years old or
above are required to use standard vehicle safety belt.

This question is in four parts. The first part is the age of a
child is 𝑎 years. Write an inequality that describes
the range of values of 𝑎 when a child must wear a seat belt when sitting in the
rear of the car.

The key to this first part of the
question is the fact that we’re told that we’re looking at a child who wears a seat
belt, that is, a seat belt, not a booster seat and not a child seat. It’s in fact using the main vehicle
seat belt. Well, to form the inequality that
we need to form, we’re gonna have two bits of information from the question, first
of all that we’re told that from the age of 18, there is no legal requirement for
passengers traveling in the backseat of a car to use the seat belt. Well, this does apply to us because
we’re told that the child is going to be sitting in the rear of the car. Also, we have another bit of
information, and that is that children at eight years old or above are required to
use standard vehicle safety belt.

Well, if for eight years or above
they have to use the standard vehicle safety belt, then what we can do is start to
form our inequality. Because we know that from eight
years and above, a child will need to wear a standard vehicle safety belt. So we can say that 𝑎 is going to
be greater than or equal to eight because it says from that eight-year point as
well, so it includes eight. However, we’re told that once they
reach 18, there is no legal requirement for them to actually wear a seatbelt. So, therefore, the inequality that
we’re looking for is 𝑎 is greater than or equal to eight but less than 18. That’s because they would have to
wear a seat belt in the back of a car all the way up to but not including 18 years
of age.

Now, what we would do is clear some
space and look at the second part of this question. So, for the second part of this
question, we’re told that the age of a child who weighs over 20 pounds is 𝑎
years. Write an inequality that describes
the range of values of 𝑎 when the child must use a forward-facing car seat or
booster seat.

The key bit of information here is
that we’re looking at a child who weighs over 20 pounds. Therefore, straightaway, we can
look at the bit of information that tells us that children age one to age three
years, inclusive, and at least 20 pounds in weight are required to be in a
forward-facing seat. So, therefore, we can start to form
our inequality because we know that 𝑎, which is the age of the child, has got to be
greater than or equal to one. And that’s because, remembering, we
were told that the child weighs over 20 pounds.

And then for the second part of our
range, well, we know that we’re looking for forward-facing car seats or booster
seats. Well, we can see that children age
four to age seven, inclusive, are required to be in a forward-facing car seat or a
booster seat. However, once the child is eight
years or above, then they only need to use a standard vehicle safety belt. So, therefore, completing our
inequality, we’ve got 𝑎 is greater than or equal to one but less than eight. Because it means that the child
must be any age up to eight but not including eight when they must be in a
forward-facing car seat or a booster seat.

So now we’ll clear some space and
move on to the third part.

A child is under four years
old. The child’s weight in pounds is
𝑤. Write an inequality that describes
the range of values of 𝑤 for which the child may travel in a forward-facing
seat.

Well, the first bit of information
that we’re told is that the child is under four years old. So, therefore, we are looking at
the second and third statements. However, what we need to consider
is the child’s weight in pounds. And what we’re considering is the
range of values of 𝑤, that weight, for which the child may travel in a
forward-facing seat.

Well, if we take a look at the
weight requirements, we can see that if the child weighs less than 20 pounds, then
they must be in a rear-facing seat. However, if they weigh at least 20
pounds, then they’re required to be in a forward-facing seat. And that is so long as they are one
year or older. So, therefore, we can say that the
inequality that satisfies our situation is 𝑤 is greater than or equal to 20. And that’s because the child must
weigh 20 pounds or more because if it’s less than 20 pounds that the child weighs,
then they must sit in a rear-facing seat.

Now, there is one more part to this
question which we’re going to look at. And again, we’ll clear some space
to do that.

A child weighs more than 20
pounds. Their age is 𝑎. Write an inequality that describes
the range of ages for which they must use a forward-facing seat.

Well, the information we’re told
here is that the child weighs more than 20 pounds. So, therefore, it means that
statement three is going to be useful for solving this problem. We’re also looking for this
situation where a child must use a forward-facing seat. So we’re also gonna take a look at
the fourth statement.

Well, first of all, we’re gonna say
that 𝑎 is greater than or equal to one. And that’s because we can see that
children age one to age three years, inclusive, and at least 20 pounds in weight are
required to be in a forward-facing seat. If they are in fact under one year
of age, then they would have to be in a rear-facing seat. But what about the upper bound of
our range?

Well, you might look at the fourth
statement and think, “Well, it’s going to be seven because it says children age four
to age seven years, inclusive, are required to be in a forward-facing car seat or a
booster seat.” However, if we look at this part of
the question, it says “What is the range of ages for which they must use a
forward-facing seat?” Well, in fact, with the fourth
statement, a child from four to seven would have the option of a forward-facing seat
or a booster seat.

So, in fact, we can say that the
inequality would be 𝑎 is greater than or equal to one but less than four. And that’s because if the child is
any age up until four, they will have to be in a forward-facing seat as long as they
are one or above. Because once they hit four, they
get that option of a forward-facing car seat or a booster seat.