Algebra I
Drill-word problem? – go over hw- 6.3 worksheet.
Group work with CW and word problems. All due tomorrow. Quiz Thursday! No
HW Tuesday or Thursday.
Period 4- Above plus Basic Practice 3 for HW. Quiz Wednesday!
SWBAT solve and graph basic and compound inequalities in an effort to solve word
problems.
Drill Algebra I
1. You started off your Saturday morning with
$15 in your pocket and you gave $3 to a
friend for lunch. Homecoming Fair games
cost $1.50 each and you have decided to play
as many as you can. Write an inequality to
describe your circumstance and determine
how many games you can play.
2. 5 < 2x – 7 < 18 Solve and graph your
answer.
Compound Inequalities
Graph the following:
1. x > 2 and x < 5
2. x < 3 or x > 4
3. -2< x< 4
4. x < -1 or x > 3
--------------
----|----|----|----|----|----|----|----|----|----|----|----|----|--
0
----------o o------
----|----|----|----|----|----|----|----|----|----|----|----|----|--
0
0---------------------------
----|----|----|----|----|----|----|----|----|----|----|----|----|--
0
----o
o------
----|----|----|----|----|----|----|----|----|----|----|----|----|--
0
Solve the following and graph the solution on the number line.
5. 5 < x + 4 < 8
1 < x <4
----|----|----|----|----|----|----|----|----|----|----|----|----|--
0 o-------------o
0
6. -2 < 3x + 4 < 13 ----|----|----|----|----|----|----|----|----|----|----|----|----|--
-6< 3x < 9
-----------------------
-2< x < 3
7. 7 + 2a > 9 or
-4a > 8
2a > 2 or a < -2
a>1
----|----|----|----|----|----|----|----|----|----|----|----|----|--
---------o
0 o-------
Inequality Word Problems
1.
2.
3.
4.
Label the variables.
Write an inequality to represent each circumstance.
Solve the inequality.
What does the answer mean in the context of the problem?
1. Suppose it takes no more than 25 min for you to get to school. After you have
traveled for 13.5 min, how much longer at most will it take you to get to
school?
X = how long it will take you to get to school
X + 13.5 < 25
X < 11.5
It will take 11.5 minutes or less to get to school.
2. Suppose you can get a higher interest rate on your savings if you maintain a
balance of at least $1000 in your savings account. The balance in your
savings account is now $1058. You deposit $44.50 into your account. What
is the largest amount you can withdraw and still get the higher interest rate?
X = amount of withdraw
1058 + 44.50 – x > 1000
1102.50 – x > 1000
-x > -102.50
x < 102.50
The most that I can withdraw is $102.50.
3. A gallon of paint will cover 600 ft2. If you have at least 2400 ft2 to paint, what
is the least number of gallons of paint you will need?
X = number of gallons of paint
600x > 2400
x.> 4
You will need at least 4 gallons of paint.
4. The Garcias are putting down a brick border along their flower garden. The
flower garden is no more than 31 ft long. If the bricks are 6 inches long, what
is the greatest number of bricks needed?
31 ft * 12 = 372 inches
x = number of bricks needed
6x < 372
x < 62
They will need at most 62 bricks.
5. Tickets to a museum cost $5 for adults and $2.50 for children. There are five
adults in the group. The total cost for the group was no more than $57.50.
What is the greatest possible number of children in the group?
X = number of children
5(5) + 2.50x < 57.50
25 + 2.50x < 57.50
2.50x < 32.50
x < 13
The most number of children that can attend is 13.
6. Beatriz is in charge of setting up a banquet hall. She has five tables that will
seat six people each. If no more than 62 people will attend, how many tables
seating four people each will she need?
X = number of 4 person tables
5(6) + 4x < 62
30 + 4x < 62
4x < 32
x<8
Beatriz only needs 8 4-person tables or less for the banquet hall.
7. The student council is sponsoring a concert as a fundraiser. Tickets are $3
for students and $5 for adults. The student council wants to raise more than
$1000. If 200 students attend, how many adults must attend?
X = number of adults that must attend
3(200) + 5x > 1000
600 + 5x > 1000
5x > 400
x > 80
The student council needs to sell more than 80 adult tickets.
8. Javier is on a diet. He is supposed to eat at least 1500 calories but no more
than 1800 calories per day. Before his last meal of the day, he has had 1150
calories. What number of calories should Javier eat at his last meal of the
day?
X = number of calories of the last meal of the day
1500 < x + 1150 < 1800
350 < x < 650
Javier needs to eat at least 350 calories, but no more than 650 in his last meal.
9. To get an A in class your total points must be between 540 and 600 inclusive.
Suppose you have 503 points before the last test. What possible values for
the last test will still give you an A in the class?
X = your score on the last test
540 < x + 503 < 600
37 < x < 97
The last test can be anywhere from a 37 to a 97, including both.
10. The drama department is putting on a play. They pay a royalty fee of $300
(for the rights to put on the play) and operating costs are $1.50 per ticket
sold. The tickets sell for $5 each. How many tickets must they sell in order to
cover their expenses?
X = number of tickets that need to be sold
300 + 1.50x < 5x
300 < 3.50x
85.7 < x
The drama department needs to sell at least 86 tickets in order to cover its
expenses.