Algebra II
Word Problems (writing equations and inequalities)
1) There are several different ways to write or show inequalities. Write each of the following in interval
notation.
a) x < -3
b) x ≥ 5
c)
d)
2) Show how you can write an inequality expression to describe each of the following situations.
a) There are fewer than 200 students in the senior class.
b) A student may enroll in no more than six courses each year.
c) To participate in a concert, you must be willing to attend at least ten rehearsals.
d) There is space for at most 165 students in the high school band.
For the following problems, define a variable, write an equation or inequality, and solve.
3) Jane is one year older than twice Tom’s age. Tom’s father, Jim, is 2 years younger than twice Jane’s
age. The mother, Kathy, is 15 years older than Jane. All together they are 107 years old. What is each
ones age?
4) The Lincoln’s hotel room costs $90 a night. An additional 10% is added (for tax). Hotel parking is $12
per day. The Lincoln’s expect to spend $30 in tips during their stay. How many nights can the Lincoln’s
stay without exceeding total cost of $600.
5) Jan’s savings account balance is $3800. Of this, $750 is rent. Jan wants to keep a balance of at least
$500. How much can she withdraw and still meet these conditions.
6) Allie borrowed some money from her friend Jackson. They agreed that she would pay him the full
amount that she borrowed as well as $0.15 per day that it takes her to repay him. If Allie borrowed $75
and ends up paying Jackson $78, how many days did it take her to repay him?
7) Lauren has at most $10.50 to spend at a convenience store. She buys a bag of potato chips and a can
of soda for $1.55. If gasoline at this store costs $1.35 per gallon, how many gallons of gas can she buy
for her car? Round to the nearest tenth of a gallon.
8) Brooke has a 91.4 in math class. She has 5 grades so far. Four of her grades are 82, 100, 88, and 95.
What is the other grade?
9) Mrs. Hoying is renting a car that gets 35 miles per gallon. The rental charge is $19.50 per day plus
$0.18 per mile. Her company will reimburse her for $33 of this portion of her travel expenses. If Mrs.
Hoying rents the car for one day, find the maximum number of miles that will be paid for by her
company.
Compound Inequalities:
10) -3 ≤ 2x + 1 < 11
11) 2x > 14 and 3x < -1
12) -3 < x+ 4 < 7
13) 2x + 7 > 5 or 2x + 7 < -3