Solving Absolute Value Equations in Real-Life Scenarios

A temperature is recorded as -5 degrees Celsius. If the absolute value of the temperature is represented by the equation |x| = 5, what are the possible values of x?

• 5, -5

• 0, 5

• -3, 3

• -10, 10

A diver is 12 meters below sea level. If the absolute value of the depth is represented by the equation |x| = 12, what are the possible heights above sea level?

• 10 meters

• 15 meters

• 12 meters, 0 meters

• -12 meters

A car travels 30 miles east and then 30 miles west. If the total distance traveled is represented by the equation |x - 30| = 30, what are the possible values of x?

• [0, 60]

• [60, 90]

• [30, 30]

• [0, 30]

A person is 4 feet away from a wall. If the distance from the wall is represented by the equation |x| = 4, what are the possible positions of the person relative to the wall?

• The person can be positioned at -4 feet (4 feet to the left of the wall) or 4 feet (4 feet to the right of the wall).

• The person can be at -6 feet or 6 feet from the wall.

• The person can be at -2 feet or 2 feet from the wall.

• The person can only be at 0 feet from the wall.

A bank account has a balance of -50 dollars. If the absolute value of the balance is represented by the equation |x| = 50, what are the possible values of x?

• 25, 75

• 50, -50

• -50, 0

• -25, 100

A runner is 15 meters behind the starting line. If the distance from the starting line is represented by the equation |x + 15| = 15, what are the possible positions of the runner?

• 0 meters, -30 meters

• -15 meters

• -45 meters

• 30 meters

A mountain climber is at an elevation of -200 meters. If the elevation is represented by the equation |x| = 200, what are the possible elevations the climber could be at?

• 0 meters and 400 meters

• 100 meters and -100 meters

• -300 meters and 300 meters

• 200 meters and -200 meters

A student scored 10 points below the average in a test. If the score difference is represented by the equation |x + 10| = 10, what are the possible scores of the student?

• [0, -20]

• -30, -40

• 10, -10

• 5, -15

A hiker is 25 miles away from the campsite. If the distance is represented by the equation |x - 25| = 25, what are the possible locations of the hiker?

• 10 miles or 40 miles

• 15 miles or 35 miles

• 5 miles or 55 miles

• 0 miles or 50 miles

A fish is swimming 8 feet below the surface of the water. If the depth is represented by the equation |x| = 8, what are the possible depths of the fish?

• -8 feet

• 0 feet

• 8 feet

• -4 feet