Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.9

Lesson 8.5Testing Solutions

Apply Day · Set BSecond form · new problems, same idea

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can graph the solutions of an inequality on a number line.

Remember8.5 · Part II

Graphing Inequalities on the Number Line

  1. Draw the boundary circle at the given constant number
  2. Open Circle (○) for < or > (boundary value is not included in solution set)
  3. Closed Circle (●) for ≤ or ≥ (boundary value is included). Shade right for >, left for <

Words: Number line (Recta numérica)Open circle (Círculo abierto)Closed circle (Círculo cerrado)Solution set (Conjunto solución)Inequality (Desigualdad)

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.
    152025303525
    Closed circle at 25, shaded to the left.

    A number line for a speed rule shows a closed circle at 25, shaded to the left. Which sentence matches it?

    1. AThe speed is at most 25 mph.
    2. BThe speed is less than 25 mph.
    3. CThe speed is at least 25 mph.
    4. DThe speed is more than 25 mph.
    Show your work
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.

    Graph x > 8. Which circle do you draw at 8: open or closed?

    Show your work
    Final answer:
  2. 3Complete each step, then write the final answer.

    Graph w ≤ 15. Which way do you shade from 15: left or right?

    Show your work
    Final answer:
  3. 4Complete each step, then write the final answer.
    67891011121314151612
    Closed circle at 12, shaded to the left.

    The number line shows a closed circle at 12, shaded to the left. It shows x ≤ 12. Which symbol goes in the box: 12 ☐ x?

    Show your work
    Final answer:
  4. 5Circle the letter of the best answer. Show how you know.

    Campers must be older than 9. Which graph shows every allowed age?

    1. AOpen circle at 9, shade right
    2. BClosed circle at 9, shade right
    3. COpen circle at 9, shade left
    4. DClosed circle at 9, shade left
    Show your work
  5. 6Complete each step, then write the final answer.

    Which whole numbers make both x > 3 and x ≤ 7 true? How many are there?

    Show your work
    Final answer:
  6. 7Circle the letter of the best answer. Show how you know.

    Which graph represents x < 5?

    1. AOpen circle at 5, shaded left
    2. BClosed circle at 5, shaded left
    3. COpen circle at 5, shaded right
    4. DClosed circle at 5, shaded right
    Show your work
  7. 8Circle the letter of the best answer. Show how you know.

    Which graph represents x ≥ 3?

    1. AClosed circle at 3, shaded right
    2. BOpen circle at 3, shaded right
    3. CClosed circle at 3, shaded left
    4. DOpen circle at 3, shaded left
    Show your work
  8. 9Circle the letter of the best answer. Show how you know.

    Which graph represents x > 8?

    1. AOpen circle at 8, shaded right
    2. BClosed circle at 8, shaded right
    3. COpen circle at 8, shaded left
    4. DClosed circle at 8, shaded left
    Show your work
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help