Algebra 1, Unit #2
Name: _____________________________
Part I: Writing, Solving, and Graphing Inequalities (PAGE 1)
Write inequalities to represent the following verbal expressions. Solve and graph #11-14 on a number line.
1
1. All real numbers x less than or equal to -7
8. The quotient of k and 9 is greater than 3
2. 6 less than a number k is greater than 13
9. All numbers x, that are over 7
3. All real numbers p, greater than or equal to 8
10. The restaurant can seat at most 172 people.
4. The sum of t and 7 is less than -3
**11. The sum of 5x and 2x is at least 14
5. 8 less than 4 times a number is less than 12
**12. 5 less than a number y is under 20
6. B is less than 4
**13. 3 less than g is less than or equal to 17
7. Seven more than a number is less than 14
**14. The difference of 12 and a number is less than 10
Write an inequality to represent each of the following graphs.
15.
______________________
16. ______________________
17.
________________________
18. ______________________
Part II: Solve the inequalities and graph your solution on the number line. Show your work.
**Some of these are special cases – “All Solutions” if always true, or “No Solutions” if never true!!**
1. −3𝑥 − 2𝑥 < 5
3.
2. 10 − 8𝑎 ≥ 2(5 − 4𝑎)
−9 ≥ −8(1 + 6𝑣) − 1
5. 6𝑚 − 5 > 7𝑚 + 7 − 𝑚
7.
𝑧−3
5
−1>
𝑧
2
**clear fractions first!
4. −1(2 + 2𝑚) − 2 > 6
6.
−2−𝑤
4
≤
1+𝑤
3
**clear fractions first!
8. 8 + 5𝑥 ≥ 7𝑥 + 2 − 2𝑥
9. 18𝑥 − 5 ≤ 3(6𝑥 − 2)
10. 3 − (2𝑥 − 3) > −8𝑥 + 2(4 + 3𝑥)
Part III: Applications: Lake Compounce, in Bristol, CT, is the oldest, continuously-operating
amusement park in North America, having opened in 1846. To ensure safety for all of its guests, the park
has regulations for the height of anyone going on a ride. In the table below, write and graph inequalities
to represent the height requirements for each of the rides. Let h represent the height of a rider.
Part IV: Writing and Solving Real – World Inequalities
Write and solve an inequality to represent each situation. Define your variable. Show your work and
describe what solution in words. ex. “They must sell 55 or more pieces of candy to make a profit…”
1. On a farm, the number of cows is 50 more than twice the number of sheep. If there are at most 260
animals in all, find the greatest number of cows, and the greatest number of sheep there could be on this
farm. x: ______________________________
2. Bob received grades of 88, 91, 89, and 87 on four science tests. What is the lowest grade that Bob can
receive on the fifth test in order for his average to be greater than 90? x: ________________________
3.
In Sara's bank, there are twice as many nickels as quarters. If the value of these coins is at least $8.05,
find the smallest possible number of nickels and quarters in her bank. x: ________________________
4.
Mary decided that she would not spend more than $275 for a new coat and dress. If the price of the
coat was $25 less than 3 times the price of the dress, what was the highest possible price of the dress?
x: ______________________________
5. At a movie theater the cost of an adult ticket is $6.00, and the cost of a child's ticket is $2.00. If at one
showing last week, 200 more adult tickets were sold than children's tickets, what is the smallest number
of each type of ticket that was sold if the total receipts from sales was at least $2400?
x: ______________________________
6. The length of a rectangle is 10" less than 2 times its width. If the perimeter of the rectangle is at most
160", find the maximum width of the rectangle. x: ______________________________
7. The cost per month of making n number of wooden toys is C = 3n + 30 . The income from selling n
toys i s I = 6n . How many toys must the company make to get a profit (I > C) ?
8. Sarah has an account on www.etsy.com where she sells homemade jewelry. She is trying to sell fifteen
pairs of earrings and one $35 necklace to raise money for a new iPad. How much should she charge for
each pair of earrings so she can have at least $200 for her iPad? x: ______________________________
9.
Matt has to pay for his lunch using his own money! He currently has $46 and lunch costs $2.25 per
day. How many days can he buy lunch and still have at least $10 left to buy a video game?
x: ______________________________
10. Amanda works at Applebee’s and earned $7.25 per hour plus $35 total in tips for the week. Sarah works
at Big Lots and makes $9 per hour. If they each work the same number of hours each week, how many
hours do they have to work for Sarah to earn more money than Amanda? x: ___________________
11. The length of a rectangle is 3 feet longer than twice the width. If the perimeter of the rectangle must
exceed 78 feet, what are all of the possible widths of the rectangle? x: ___________________________