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

Lesson 8.68.6 · Part II

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can solve an inequality and graph its solution set on a number line.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
SolveSpanish: Resolver To find the number that makes it true. x + 3 > 10 → subtract 3 → x > 7 — any number greater than 7 works
GraphSpanish: Graficar To show answers on a number line with circles and shading. x > 7: open circle at 7, shade right — shows all solutions at a glance
SolutionSpanish: Solución A number that makes the equation or inequality true. x = 8 is a solution to x > 7 because 8 > 7 is true; x = 5 is not because 5 > 7 is false
SubstituteSpanish: Sustituir To put a number in place of a letter. Substitute x = 5 into x + 3 > 10: 5 + 3 = 8, and 8 > 10 is false, so x = 5 is not a solution
Solution setSpanish: Conjunto solución All the numbers that make the inequality true. For x > 4, the solution set is every number greater than 4, such as 5, 6, 7, ...
Inverse operationSpanish: Operación inversa Two math actions that undo each other, like × and ÷. To solve x + 3 > 7, use the inverse of adding 3: subtract 3 to get x > 4.

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

Word bank SolveGraphSolutionSubstituteSolution setInverse operation

Watch outA common mistake

A common mistake in Solve and Graph Inequalities is shading the number line in the wrong direction after solving. For example, a student solves x + 4 > 10 correctly to get x > 6, but then shades LEFT toward smaller numbers instead of RIGHT toward greater numbers. The shading direction always matches the solved symbol, not the original problem: '>' and '≥' shade right (greater numbers), '<' and '≤' shade left (smaller numbers) — check this AFTER you solve, not before. To catch this mistake, substitute one shaded value and one unshaded value back into the original inequality: the shaded value should make it true, and the unshaded value should make it false.

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

Lesson 8.68.6 · Part II

Apply Day · Version ASupported practice

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

Learning target I can solve an inequality and graph its solution set on a number line.

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

    Solve x + 4 > 11. What is the boundary number?

    Show your work

    Hint 4 is added to x. Subtract 4 from both sides.

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

    Solve x − 3 ≤ 9. What is the boundary number?

    Show your work

    Hint 3 is subtracted from x. Add 3 to both sides.

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

    Solve x + 8 ≥ 20. What is the smallest value of x that makes it true?

    Show your work

    Hint Subtract 8 from both sides. The symbol ≥ includes the boundary number.

    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.68.6 · Part II

Apply Day · Version BCore practice

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

Learning target I can solve an inequality and graph its solution set on a number line.

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

    Eli solves x + 9 < 15 and gets x < 24. Is he right? What is the boundary number?

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

    Solve 6x ≥ 45. What is the boundary number?

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

    Solve x − 6 < 9. What is the boundary number?

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.68.6 · Part II

Apply Day · ChallengeExtension

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

Learning target I can solve an inequality and graph its solution set on a number line.

  1. 1Circle the letter of the best answer. Show how you know.

    Solve n − 6 > 9. Which number line shows the solution set?

    1. AAn open circle at 3 with shading to the right
    2. BAn open circle at 15 with shading to the right
    3. CA closed circle at 15 with shading to the right
    4. DAn open circle at 15 with shading to the left
    Show your work
  2. 2Complete each step, then write the final answer.

    Kim and Lou solve 5x > 30. Kim gets x > 6. Lou gets x > 150. What is the boundary number?

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

    Solve 8x ≤ 52. What is the boundary number?

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help