Question

in 1 - 14, write an inequality for each situation.

1. the number of students the bus holds, s, is less than 40.
2. the weight limit, w, on the bridge is 12 tons.
3. the distance, d, is at least 110 miles.
4. the depth of the swimming pool, d, cannot be deeper than 3\frac{1}{2} feet.
5. the least amount of water, w, that hikers must bring is 30 ounces.
6. the fewest number of minutes, m, that a player must practice per day is 45 minutes.
7. tims age, t, is not 21 years old.
8. the cost, c, is less than $45.
9. the length of the driveway, d, is longer than \frac{1}{5} mile.
10. the height of the sunflower, s, is not 45\frac{5}{6} inches tall.
11. a persons height, h, must be at least 48 inches tall to go on this ride.
12. leonard submitted p photographs in an art show. he did not submit 5 photographs.
13. gabe has 6 more baseball cards than football cards. he has fewer than 125 baseball cards. write an inequality for the number of football cards, f, he has.
14. if the sub shop sells at least 35 subs in a day, they make a profit. write an inequality for the number of subs, s, they must sell in a day to make a profit.

Explanation:

Step1: Translate "less than"

For the first situation: "The number of students the bus holds, \(s\), is less than 40". The symbol for "less than" is \( < \). So the inequality is \(s<40\).

Step2: Translate "weight limit"

For the second situation: "The weight limit, \(w\), on the bridge is 12 tons". A weight limit means the weight \(w\) can be at most 12. The symbol for "at most" (or "less than or equal to") is \( \leq \). So the inequality is \(w\leq12\).

Step3: Translate "at least"

For the third situation: "The distance, \(d\), is at least 110 miles". The symbol for "at least" (or "greater than or equal to") is \( \geq \). So the inequality is \(d\geq110\).

Step4: Translate "cannot be deeper than"

For the fourth situation: "The depth of the swimming pool, \(d\), cannot be deeper than \(3\frac{1}{2}\) feet". "Cannot be deeper than" means "less than or equal to". \(3\frac{1}{2}=\frac{7}{2}\). So the inequality is \(d\leq\frac{7}{2}\).

Step5: Translate "the least amount"

For the fifth situation: "The least amount of water, \(w\), that hikers must bring is 30 ounces". "The least amount" means "greater than or equal to". So the inequality is \(w\geq30\).

Step6: Translate "the fewest number"

For the sixth situation: "The fewest number of minutes, \(m\), that a player must practice per day is 45 minutes". "The fewest number" means "greater than or equal to". So the inequality is \(m\geq45\).

Step7: Translate "is not"

For the seventh situation: "Tim's age, \(t\), is not 21 years old". "Is not" means \(t
eq21\).

Step8: Translate "less than"

For the eighth situation: "The cost, \(c\), is less than \(\$45\)". The symbol for "less than" is \( < \). So the inequality is \(c < 45\).

Step9: Translate "longer than"

For the ninth situation: "The length of the driveway, \(d\), is longer than \(\frac{1}{5}\) mile". The symbol for "longer than" (or "greater than") is \( > \). So the inequality is \(d>\frac{1}{5}\).

Step10: Translate "is not"

For the tenth situation: "The height of the sunflower, \(s\), is not \(45\frac{5}{6}\) inches tall". \(45\frac{5}{6}=\frac{45\times6 + 5}{6}=\frac{275}{6}\). "Is not" means \(s
eq\frac{275}{6}\).

Step11: Translate "at least"

For the eleventh situation: "A person's height, \(h\), must be at least 48 inches tall to go on this ride". The symbol for "at least" (or "greater than or equal to") is \( \geq \). So the inequality is \(h\geq48\).

Step12: Translate "did not submit"

For the twelfth situation: "Leonard submitted \(p\) photographs in an art show. He did not submit 5 photographs". "Did not submit 5" means \(p
eq5\).

Step13: Translate "more...than" and "fewer than"

For the thirteenth situation: "Gabe has 6 more baseball cards than football cards. He has fewer than 125 baseball cards". If the number of football cards is \(f\), then the number of baseball cards is \(f + 6\). "Fewer than" means \(f+6<125\).

Step14: Translate "at least"

For the fourteenth situation: "If the sub shop sells at least 35 subs in a day, they make a profit. Write an inequality for the number of subs, \(s\), they must sell in a day to make a profit". "At least" means \( \geq \). So the inequality is \(s\geq35\).

Answer:

1. \(s < 40\)
2. \(w\leq12\)
3. \(d\geq110\)
4. \(d\leq\frac{7}{2}\)
5. \(w\geq30\)
6. \(m\geq45\)
7. \(t

eq21\)

1. \(c < 45\)
2. \(d>\frac{1}{5}\)
3. \(s

eq\frac{275}{6}\)

1. \(h\geq48\)
2. \(p

eq5\)

1. \(f + 6<125\)
2. \(s\geq35\)