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Unit 1: Relationships between Quantities – Creating Linear Equations In One Variable
Standards: MMC9-12.N.Q.3
EXERCISE 1: Translate the verbal sentences into an algebraic inequality.
a) x is at most 50
x ≤ 50
b) The sum of 5x and 2x is at least 70
c) The maximum value of 4x – 6 is 54
5x + 2x ≥ 70 (or 7x ≥ 70)
4x – 6 ≤ 54
EXERCISE 2: Translate and solve the verbal sentences.
n–6>4
Twice a number increased by 6 is at least 35 2n + 6 ≥ 35
a) 6 less than a number is greater than 4
b)
Translate each phase into an algebraic inequality.
a) A tour bus can seat 55 passengers.
P (passengers) ≤ 55
b) An energy-efficient lamp can only be used with light bulbs that are 60 watts or less.
L ≤ 60
c) Camilla is saving to purchase a new pair of bowling shoes that will cost at least $39. She
has already saved $19. What is the least amount of money she needs to save for the
shoes?
C – 19 ≤ 39
d) Suppose you earn $20 per hour working part time at a tax office. You want to earn at
least $1,800 this month, before taxes. How many hours must you work?
20h ≥ 1800
e) Hiram earned a score of 83 on his semester algebra test. He needs to have a total of at
least 180 points from his semester and final tests to receive an A for his grade. What
score must Hiram earn on his final test to ensure his A? G + 83 ≥ 180
f) Claire purchases DVDs from an online entertainment store. Each DVD that she orders
costs $15 and shipping for her order is $10.00 Claire can spend no more than $100.
How many DVDs can Claire purchase? 15d + 10 ≤ 100
EXERCISE 3: Write an inequality and solve the problem algebraically.
a. The product of nine and x is greater than six more than the product of three and x.
9x > 3x + 6. x > 1
b. Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay
her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. What is
the minimum amount of hours she will need to babysit in order for her to buy her
calculator? 5h + 10 ≥ 100. h ≥ 18 hours (discuss labels)
c. Mrs. Scott decided that she would spend no more than $120 to buy a jacket and a skirt.
If the price of the jacket was $20 more than 3 times the price of the skirt. Find the
highest possible price of the skirt?
J + S ≤ $120. J = 3S + 20. S + 3S + 20 ≤ 120. S ≤ $25 (discuss labels)
d. Stephanie weighs 3 times as much as Rachel. Both weights are whole numbers and the
sum of their weights is less than 160 pounds. Find the greatest possible weight for each
girl. S = 3R S, R  N. S + R < 160. 3R + R < 160. Max R = 39 lbs. Max S = 117 lbs.
Sum = 156
e. Mr. Diaz wishes to save at least $1500 in 12 months. If she saved $300 during the first 4
months, what is the least possible average amount that he must save in each of the
remaining 8 months? 8S + 300 ≥ 1500 . S ≥ $150
f. The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour plus
$55 for an assistant. The committee wants to keep the total cost under $600. What is
the maximum amount of hours the DJ will play at the dance? 125h + 55 < 600. h <
4.36 hours. Or 4 hours and 21.6 minutes. Needs interpretation with students
g. Six more than two times a certain number is less than the number increased by twenty.
Find the numbers that satisfy this condition. 2n + 6 < n + 20. n < 14
h. CHALLENGE: Two consecutive even integers are such that their sum is greater than 98
decreased by twice the larger. Find the smallest possible values for the integers.
2n + (2n + 2) ≥ 98 – 2 (2n +2).