Absolute Value Equations & Inequalities

Multiple Choice

The temperature at noon in Turlock on a summer day was 77°F. Throughout the day, the temperature varied from this by as much as 8 °F. Write an absolute-value to represent the range of possible temperatures for that day.

• $$\left|x-77\right|=8$$  

• $$\left|x-8\right|=77$$  

• $$\left|x-8\right|\le77$$  

• $$\left|x-77\right|\le8$$  

Multiple Choice

A carpenter is cutting boards for a shelving unit. Each board is supposed to be 85 centimeters long, but the length is allowed to differ from that by at most 0.2 cm. Write an absolute-value to represent the board lengths that would be unacceptable.

• $$\left|x-85\right|<0.2$$  

• $$\left|x-85\right|>0.2$$  

• $$\left|x-85\right|=0.2$$  

• $$\left|x-85\right|\ge0.2$$  

Multiple Choice

The drama club set a goal for each member to sell 20 tickets to their play. The students with the highest and lowest actual sales were exactly 11 tickets from this goal. Write an absolute-value to represent both the highest and lowest number of tickets sold by an individual.

• $$\left|x-11\right|=20$$  

• $$\left|x-11\right|\ge20$$  

• $$\left|x-11\right|>20$$  

• $$\left|x-20\right|=11$$  

Multiple Choice

The owner of a butcher shop keeps the freezer at −5 °C. It is acceptable for the temperature to be above or below this by as much as 1.5 °C. Write an absolute-value to represent the range of acceptable temperatures for the freezer.

• $$\left|x-5\right|\le1.5$$  

• $$\left|x+5\right|<1.5$$  

• $$\left|x+5\right|\le1.5$$  

• $$\left|x-5\right|<1.5$$  

Multiple Choice

Lucia sets the thermostat in the apartment to 68 degrees. The actual temperature in the apartment can vary from this by as much as 3 degrees. Write an absolute- value to represent the lowest and highest temperatures that occur in the apartment.

• $$\left|x-68\right|=3$$  

• $$\left|x-3\right|=68$$  

• $$\left|x-68\right|\le3$$  

• $$\left|x-3\right|\le68$$  

Multiple Choice

Rani is selling her car, which gets around 24 mpg (miles per gallon). However, her gas mileage varies from this by up to (but not including) 6 miles per gallon depending on where and how she drives. Write an absolute-value to represent the range of her car's gas mileage.

• $$\left|x-24\right|\le6$$  

• $$\left|x-24\right|<6$$  

• $$\left|x-24\right|=6$$  

• $$\left|x-24\right|\ge6$$  

Multiple Choice

At Klondike Trout Farm, most of the trout have a length of 9.25 inches. The length of some of the trout differs from this by no more than 0.75 inches. Write an absolute-value to represent the range of lengths of the trout.

• $$\left|x-0.75\right|\le9.25$$  

• $$\left|x-0.75\right|<9.25$$  

• $$\left|x-9.25\right|\le0.75$$  

• $$\left|x-9.25\right|<0.75$$  

Multiple Choice

According to the World Health Organization, water temperatures ranging from 78 to 86 degrees Fahrenheit (inclusive) are generally comfortable and safe for those exercising in a swimming pool. Write an absolute-value to represent this range of temperatures.

https://apps.who.int/iris/handle/10665/43336

• $$\left|x-4\right|=82$$  

• $$\left|x-86\right|<78$$  

• $$\left|x-78\right|=8$$  

• $$\left|x-82\right|\le4$$  

Multiple Choice

Though there are many factors that affect student achievement, a commonly discussed factor is class size. In 2020, the average class size in United States high schools ranged from 29 students (Utah) down to 17 students (Maine). Write an absolute-value to represent the range of average class sizes that year.

With an average of 25 students per class, Minnesota ranked sixth highest.

https://www.zippia.com/advice/states-most-crowded-schools-largest-classes/

• $$\left|x-23\right|\ge6$$  

• $$\left|x-23\right|\le6$$  

• $$\left|x-29\right|\le17$$  

• $$\left|x-25\right|<29$$  

Multiple Choice

A pedestrian bridge is 53 meters long. Due to changes in temperature, the bridge may expand or contract by as much as 21 millimeters. Write an absolute-value to represent the minimum and maximum lengths of the bridge.

• $$\left|x-53\right|=21$$  

• $$\left|x-21\right|=53$$  

• $$\left|x-53\right|=.021$$

• $$\left|x-53\right|\le.021$$

Multiple Choice

Write an absolute-value to represent the recommended minimum and maximum daily intakes of iron.

• $$\left|x-31.5\right|=13.5$$  

• $$\left|x-13.5\right|=31.5$$  

• $$\left|x-18\right|=45$$  

• $$\left|x-45\right|=18$$  

Multiple Choice

A jewelry maker cuts pieces of wire to shape into earrings. The equation $$\left|x-18\right|=1.1$$  gives the minimum and maximum lengths in centimeters of the wires used for various designs. Calculate the shortest length of wire used.

• 1.1 cm

• 16.9 cm

• 19.1 cm

• 16.9 and 19.1 cm

Open Ended

Type which of the following (and anything else) you have done to prepare for Friday's quiz.

notes, examples, practice, ask questions, compare work with a classmate, ...