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

Lesson 8.6Solve and Graph Inequalities

Set B · Version ASecond form · supported 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.

Why This Matters Detective Kim knows that the suspect withdrew more than $50 from an ATM. The amount plus a $3 fee totaled more than $53. She writes x + 3 > 53 and needs to solve for x, then graph the solution set to share with the bank. How can she find and display all possible withdrawal amounts?

RememberSolve and Graph Inequalities

Solving & Graphing One-Step Inequalities I solve an inequality the same way as an equation: use inverse operations to get the variable alone. But the answer is a range of values, so I show all of them on a number line.

Isolate the variable using inverse operations on both sides (same as equations).
Write the simplified inequality with the variable on the left (e.g. x > 5).
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)

1Circle the letter of the best answer. Show how you know.
Which graph represents x > 8?
1. AClosed circle at 8, shaded right
2. BOpen circle at 8, shaded right
3. COpen circle at 8, shaded left
4. DClosed circle at 8, shaded left
Show your work
2Circle the letter of the best answer. Show how you know.
Which graph represents x ≤ 10?
1. AOpen circle at 10, shaded left
2. BClosed circle at 10, shaded left
3. CClosed circle at 10, shaded right
4. DOpen circle at 10, shaded right
Show your work
3Circle the letter of the best answer. Show how you know.
Which graph represents x < 5?
1. AClosed circle at 5, shaded left
2. BOpen circle at 5, shaded right
3. COpen circle at 5, shaded left
4. DClosed circle at 5, shaded right
Show your work
4Circle the letter of the best answer. Show how you know.
A detective needs at least $75 for a surveillance camera. She has already saved $48. The inequality 48 + s ≥ 75 represents how much more money s she needs. Solve 48 + s ≥ 75.
1. As ≥ 27
2. Bs ≤ 27
3. Cs ≥ 75
4. Ds ≥ 123
Show your work
5Circle the letter of the best answer. Show how you know.
A detective needs at least $75 for a surveillance camera. She has already saved $48. The inequality 48 + s ≥ 75 represents how much more money s she needs. Is exactly $27 enough?
1. ANo — she needs more than 27
2. BYes — 'at least' includes 27 exactly
3. CNo — she needs 75
4. DOnly if she saves more
Show your work
6Circle the letter of the best answer. Show how you know.
A detective needs at least $75 for a surveillance camera. She has already saved $48. The inequality 48 + s ≥ 75 represents how much more money s she needs. How is s ≥ 27 graphed?
1. AClosed circle at 27, shaded to the right
2. BOpen circle at 27, shaded to the right
3. CClosed circle at 27, shaded to the left
4. DOpen circle at 27, shaded to the left
Show your work

Explain your thinkingHow is solving an inequality similar to and different from solving an equation?

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

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked

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 8.6Solve and Graph Inequalities

Set B · Version BSecond form · core 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.

Part 1Understand the ideamodels and meaning

1Write the name of the correct group on each line.
Detective, sort each suspect's badge number into the right vault door for the rule x ≥ 4. A value is a solution if it makes x ≥ 4 true.

Groups: Solution of x ≥ 4 NOT a solution of x ≥ 4
- 9
- 5
- 4
- 3
- 2
- 0
2Write the letter of the matching item on each line.
Match each inequality to the equivalent inequality written with the number first. Both inequalities in a pair must have the same solutions.
1. x > 10
2. x ≤ 6
3. x ≥ 8
4. x < 5
- A10 < x
- B6 ≥ x
- C8 ≤ x
- D5 > x
3Circle the letter of the best answer. Show how you know.
Final gate — describe the solution set. The vault rule is x > 7. What does the solution set mean?
1. AAll numbers greater than 7
2. BOnly the number 7
3. CAll numbers less than 7
4. DEvery number, including 7
Show your work

Part 2Apply itreal-world problems

4Circle the letter of the best answer. Show how you know.
Clue 1: Which value is a solution of x > 7?
1. A3
2. B5
3. C7
4. D9
Show your work
5Circle the letter of the best answer. Show how you know.
Clue 2: Is 5 a solution of x ≤ 5?
1. AYes, because 5 ≤ 5 is true
2. BNo, because 5 is not less than 5
3. CNo, because ≤ means only smaller numbers
4. DYes, but only because 5 is odd
Show your work

Part 3Explain and correctreasoning

6Find the mistake. Explain it, then show the correct work.
Level 2 Extension — Catch the Boundary Mistake
1. 1Vault rulex > 7
2. 2Test the boundary valueSubstitute x = 7: 7 > 7
3. 3Rookie's conclusion7 > 7 is true, so 7 IS a solution and opens the gate.
4. 4Mark the solution setThe detective adds 7 to the list of solutions.
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:

Explain your thinkingHow is solving an inequality similar to and different from solving an equation?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked

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