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Algebra 1

2.9.8 Practice

Algebra 12.9.8 Practice
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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.

  • x = − 3
  • x = − 2
  • x = − 1
  • x = 0
  • x = 1
  • x = 2
  • x = 3

2. 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.
  1. D.
  2. C.
  3. B.
  4. A.

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.


3. 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.

4. 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.

5. The equation 20𝑥 = 5𝑥+60 represents a possible constraint about the situation. Solve for 𝑥. 𝑥= ____
6. Which shop offers more membership points if you rent a bike for longer than the constraint you found in the previous question?
  1. Bikes Unlimited
  2. Cycle Rentals

7. 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. D.
  2. C.
  3. B.
  4. A.

8. Which number line represents the solution to 5 + 8 x < 3 ( 2 x + 4 ) ?

  1. D.
  2. C.
  3. B.
  4. A.
9. 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

10. 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 = ____

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