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

Lesson 8.68.6 · Part II

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

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
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Learning target I can solve an inequality and graph its solution set on a number line.

Remember8.6 · Part II

Solving & Graphing One-Step Inequalities

  1. Isolate the variable using inverse operations on both sides (same as equations)
  2. Write the simplified inequality with the variable on the left (e.g. x > 5)
  3. Graph the solution set on a number line with open/closed circle and arrow shading

Words: Solve (Resolver)Graph (Graficar)Solution (Solución)Substitute (Sustituir)Solution set (Conjunto solución)

  1. 1Complete each step, then write the final answer.

    Solve x + 5 > 12. What is the boundary number?

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

    Solve x − 18 ≥ 25. What is the smallest value of x that makes it true?

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

    Solve x ÷ 2.5 < 4. What is the boundary number?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    A bus can carry at most 40 people. 23 people are already on it. Write and solve an inequality for the number of people p who can still get on. What is the greatest number?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    An elevator can carry at most 1,200 pounds. Each box weighs 75 pounds. Write and solve an inequality for the number of boxes b. What is the greatest number of boxes?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Solve x + 4.5 ≤ 3 × 4. What is the boundary number?

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

    Solve: x + 6 > 14

    1. Ax > 8
    2. Bx < 8
    3. Cx = 8
    4. Dx > 20
    Show your work
  8. 8Circle the letter of the best answer. Show how you know.

    Solve: x − 9 ≤ 3

    1. Ax ≤ 6
    2. Bx ≤ 12
    3. Cx ≥ 12
    4. Dx = 12
    Show your work
  9. 9Circle the letter of the best answer. Show how you know.

    Solve: x + 10 ≥ 25

    1. Ax ≥ 15
    2. Bx ≤ 15
    3. Cx = 15
    4. Dx ≥ 35
    Show your work
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