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

Lesson 8.68.6 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can solve an inequality and graph its solution set on a number line — one step at a time, with support.

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.

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Solve x + 3 > 53. Then graph the solution.

  1. Subtract 3 from both sides: x > 53 − 3
  2. Subtract to find the boundary: 53 − 3 = 50 → x > 50
  3. Draw an open circle at 50: > → open circle
  4. Shade to the right: x > 50 → shade right
  5. Check with a value from the shaded part: 60 + 3 = 63 → 63 > 53 ✓
  6. x > 50. Open circle at 50, shaded to the right.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Solve x − 5 ≤ 8. Then graph the solution.

Answer:

Say it and write itSentence starters

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

  • Solving an inequality is like solving an equation because I still use , but it is different because the answer is instead of .

Word bank SolveGraphSolutionSubstituteSolution setInverse operationinverse operationsmany valuesone valuegraphsolution setnumber line

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 Small Group · Group 1

Group 1Supported practice

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

Learning target With my small group, I can solve an inequality and graph its solution set on a number line — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    891011121314151617181920test 16
    Find the boundary. Then graph it.

    Solve x + 6 > 20. Then graph the solution.

    1. 1Subtract 6 from both sides. What is 20 − 6?
    2. 2Write the solution. Is 14 included?
    3. 3Which circle do we draw? Which way do we shade?
    4. 4Test x = 16. Is 16 + 6 greater than 20?
    Final answer:
  2. 2Complete each step, then write the final answer.
    45678910111213141516test 9
    Find the boundary. Then graph it.

    Solve x − 7 ≤ 4. Then graph the solution.

    1. 1What is the inverse of subtracting 7?
    2. 2Add 7 to both sides. What is the boundary number?
    3. 3Which circle do we draw? Which way do we shade?
    4. 4Test x = 9. Is 9 − 7 less than or equal to 4?
    Final answer:
  3. 3Complete each step, then write the final answer.

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

    Show your work

    Hint 5 is added to x. Subtract 5 from both sides.

    Final answer:
  4. 4Complete 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

    Hint 18 is subtracted from x. Add 18 to both sides. Does ≥ include the boundary?

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

    Ana can spend at most $50 on gifts. She already spent $32. Write and solve an inequality for the amount g she can still spend. What is the most she can spend?

    Show your work

    Hint What she spent plus what she can still spend is at most 50. Write 32 + g ≤ 50.

    Final answer:
  6. 6Complete 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

    Hint Test Eli's answer with x = 20. Is 20 + 9 < 15? Then undo the + 9.

    Final answer:

Explain your thinkingHow is solving x + 6 > 20 like solving x + 6 = 20? How is the answer different?

Sentence starter The steps are the same because I ___. · The answer is different because ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help