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Practice

2.9.8 Practice

2.9.8 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

  1. Here is an inequality: 7 x + 6 2 ≤ 3 x + 2
    Select two of the values that are a solution to the inequality.
    1. x = − 3
    2. x = − 2
    3. x = − 1
    4. x = 0
    5. x = 1
    6. x = 2
    7. x = 3
  1. Which number line is represented by the inequality x ≤ 6 ?
  1. A number line is shown. There is an open circle on 6. The number line to the right of 6 is highlighted.
  2. A number line is shown. There is a closed circle on 6. The number line to the left of 6 is highlighted.
  3. A number line is shown. There is an open circle on 6. The number line to the left of 6 is highlighted.
  4. A number line is shown. There is a closed circle on 6. The number line to the right of 6 is highlighted.

For questions 3 – 4, use the following information:

Scooter rental company A charges $9 per hour plus a $11 initiation fee. Scooter rental company B charges $15 per hour.

  1. A customer writes the following inequality to represent the situation: 9 h + 11 > 15 h .
    Which of the following is true about the given inequality?
  1. h represents the number of scooters rented.
  2. Company A costs the same as Company B.
  3. Company A costs less than Company B.
  4. Company A costs more than Company B.
  1. For which number of hours does Company B cost less?
  1. 4 hours
  2. 3 hours
  3. 2 hours
  4. 1 hour

For questions 5 – 7, use the following information:

Cycle Rentals offers 20 membership points for each day that a customer rents a bike. Bikes Unlimited offers 5 membership points for each day that a customer rents a bike plus 60 points for joining the membership club.

  1. The equation 20 x = 5 x + 60 represents a possible constraint about the situation. Solve for x . x = ____.
  1. Which shop offers more membership points if you rent a bike for longer than the constraint you found in the previous question?
  1. Cycle Rentals
  2. Bikes Unlimited
  1. Which number line represents the solution to the inequality, 20 x > 5 x + 60 , representing the situation when you earn more membership points at Cycle Rentals?
  1. A number line is shown from 2 to 6 with an open circle on the point 4. The number line to the right of 4 is shaded.
  2. A number line is shown from 2 to 6 with a closed circle on the point 4. The number line to the right of 4 is shaded.
  3. A number line is shown from 2 to 6 with a closed circle on the point 4. The number line to the left of 4 is shaded.
  4. A number line is shown from 2 to 6 with an open circle on the point 4. The number line to the left of 4 is shaded.
  1. Which number line represents the solution to 5 + 8 x < 3 ( 2 x + 4 ) ?
  1. Find the solution set to this inequality by solving the related equation: 2 x − 3 > 2 x − 5 2 .
  1. x ≥ 1 2
  2. x ≤ 1 2
  3. x > 1 2
  4. x < 1 2
  1. Here is an inequality: − 10 + x 4 + 5 ≥ 7 x − 5 3 . What value of x will produce equality (or make the two sides equal)?
  • x = ____