Opening the book…
Practice Makes Progress
In the following exercises, graph each inequality on the number line and write in interval notation.
\(x > 3\)
\(x \le -0.5\)
\(x \ge \dfrac{1}{3}\)
\(x \le 5\)
\(x \ge -1.5x\)
In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.
\(m-45 \le 62\)
\(v+12>3\)
\(b+\dfrac{7}{8} \ge \dfrac{1}{6}\)
\(g-\dfrac{11}{12}<-\dfrac{5}{18}\)
\(9s \ge 81\)
\(-8v \le 96\)
\(40<\dfrac{5}{8}k\)
\(\dfrac{9}{4}g \le 36\)
\(9p>14p-18\)
\(9y+5(y+3) < 4y-35\)
\(4x-(x-2) \ge 7x-26\)
\(6n-12(3-n) \le 9(n-4)+9n\)
\(9u+5(2u-5) \ge 12(u-1)+7u\)
\(\dfrac{5}{6}a-\dfrac{1}{4}a > \dfrac{7}{12}a+\dfrac{2}{3}\)
\(12v+3(4v-1) \le 19(v-2)+5v\)
\(35k \ge -77\)
\(18q-4(10-3q) < 5(6q-8)\)
\(-\dfrac{21}{8}y \le -\dfrac{15}{28}\)
\(d+29 > -61\)
\(\dfrac{n}{13} \le -6\)
In the following exercises, translate and solve the given problems. Then write the solution in interval notation and graph on the number line.
Six more than \(k\) exceeds 25
Twelve less than \(x\) is no less than 21
Negative two times \(s\) is lower than 56
Everyday Math
A water taxi has a maximum load of 1,800 pounds. If the average weight of one person is 150 pounds, how many people can safely ride in the water taxi?
Arleen got a $20 gift card for the coffee shop. Her favorite iced drink costs $3.79. What is the maximum number of drinks she can buy with the gift card?
Joni sells kitchen aprons online for $32.50 each. How many aprons must she sell next month if she wants to earn at least $1,000?
Keshad gets paid $2,400 per month plus 6% of his sales. His brother earns $3,300 per month. For what amount of total sales will Keshad’s monthly pay be higher than his brother’s monthly pay?
Katherine is a personal chef. She charges $115 per four-person meal. Her monthly expenses are $3,150. How many four-person meals must she sell in order to make a profit of at least $1,900?
Five student government officers want to go to the state convention. It will cost them $110 for registration, $375 for transportation and food, and $42 per person for the hotel. There is $450 budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge $5 per car, how many cars must they wash in order to have enough money to pay for the trip?
In 2014, a high school stage collapsed in Fullerton, California, when 250 students got on stage for the finale of a musical production. Two dozen students were injured. The stage could support a maximum of 12,750 pounds. If the average weight of a student is assumed to be 140 pounds, what is the maximum number of students who could safely be on the stage?
Adele and Walter found the perfect venue for their wedding reception. The cost is $9,850 for up to 100 guests, plus $38 for each additional guest. How many guests can attend if Adele and Walter want the total cost to be no more than $12,500?
Writing Exercises
Find your last month’s phone bill and the hourly salary you are paid at your job. (If you do not have a job, use the hourly salary you would realistically be paid if you had a job.) Calculate the number of hours of work it would take you to earn at least enough money to pay your phone bill by writing an appropriate inequality and then solving it.
Self Check
Use this checklist to evaluate your mastery of the objectives of this section.
If most of your checks were:
…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them.
…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is crucial to establish a strong foundation before proceeding. Who can you ask for help? Your classmates, tutors, and class instructor are good resources.
…no - I don’t get it! This is a warning sign, and you must not ignore it. You should get help right away, or you will quickly be overwhelmed. Meet with your instructor during their drop-in hours as soon as you can to discuss your situation. Together, you can devise a plan to get the help you need.
This page titled Section 0.4P: Practice was last modified on Mon, 08 Dec 2025 22:18:29 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Math Department.
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