Question

activity 32
write an inequality, using x to represent an unknown number. solve. remember: ≤ means \less than or equal to.\ ≥ means \greater than or equal to.\
the number of actors in a play is less than 10.
the tax on an item equals 15 or is less than 15.
there are over 250 pages in a new book.
each team has more than 15 players.
the area has at least 5 local tv stations.
the number of players on each team is at most 5.
a father 60 years old is more than twice the age of his daughter.
a mother 50 years old is not more than twice the age of her son.
the high temperature was more than 5° above freezing, 32°f.
there were fewer than 37 persons at a board meeting.
a catch of 5 fish was not in excess of half the limit.
twice the number of miles driven the first day is not more than 250.
they expect to sell at least 250 tickets for the school play.
the cost of a pencil is less than one - third the cost of a 75 - cent pen.
a student agrees to work no more than 20 hours per week on a part - time job.
algebra by design / russell f. jacobs
www.tessellations.com
© 1994 jacobs publishing co. / 2011 tessellations

Explanation:

Step1: Translate statements to inequalities

For "The number of actors in a play is less than 10", if we let \(x\) be the number of actors, then \(x < 10\).
For "The tax on an item equals 15 or is less than 15", if \(x\) is the tax, then \(x\leq15\).
For "There are over 250 pages in a new book", if \(x\) is the number of pages, then \(x > 250\).
For "Each team has more than 15 players", if \(x\) is the number of players per - team, then \(x>15\).
For "The area has at least 5 local TV stations", if \(x\) is the number of local TV stations, then \(x\geq5\).
For "The number of players on each team is at most 5", if \(x\) is the number of players per - team, then \(x\leq5\).
For "A father 60 years old is more than twice the age of his daughter", if \(x\) is the daughter's age, then \(60>2x\).
For "A mother 50 years old is not more than twice the age of her son", if \(x\) is the son's age, then \(50\leq2x\).
For "The high temperature was more than 5° above freezing, 32°F", if \(x\) is the high - temperature, then \(x > 32 + 5=37\).
For "There were fewer than 37 persons at a board meeting", if \(x\) is the number of persons at the meeting, then \(x < 37\).
For "A catch of 5 fish was not in excess of half the limit", if \(x\) is the catch limit, then \(5\leq\frac{x}{2}\).
For "Twice the number of miles driven the first day is not more than 250", if \(x\) is the number of miles driven the first day, then \(2x\leq250\).
For "They expect to sell at least 250 tickets for the school play", if \(x\) is the number of tickets sold, then \(x\geq250\).
For "The cost of a pencil is less than one - third the cost of a 75 - cent pen", if \(x\) is the cost of the pencil, then \(x<\frac{75}{3}=25\) (assuming cost in cents).
For "A student agrees to work no more than 20 hours per week on a part - time job", if \(x\) is the number of hours worked per week, then \(x\leq20\).

Answer:

1. \(x < 10\)
2. \(x\leq15\)
3. \(x > 250\)
4. \(x>15\)
5. \(x\geq5\)
6. \(x\leq5\)
7. \(60>2x\)
8. \(50\leq2x\)
9. \(x > 37\)
10. \(x < 37\)
11. \(5\leq\frac{x}{2}\)
12. \(2x\leq250\)
13. \(x\geq250\)
14. \(x < 25\)
15. \(x\leq20\)