# Question Video: Creating Linear Inequalities with One Variable Mathematics

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 back seat of a car to use a seat belt. Children under 1 year of age and children weighing less than 20 lb are required to be in a rear-facing seat. Children age 1 to age 3 years (inclusive) and at least 20 lb in weight are required to be in a forward-facing seat. Children age 4 to age 7 years (inclusive) are required to be in a forward-facing car seat or a booster seat. Children at 8 years old or above are required to use standard vehicle safety belt. 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.

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### 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.