6.AT.8 Lesson 8-6-part2 Apply Day · Practice
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.6 · Part II

Application Practice for Today's Problem

Solve and Graph Inequalities · Solve

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 8.6 · Part II
1Solving & Graphing One-Step Inequalities
2Strategy Model — step by step
  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
3Mathematical Word Bank
  • Solve and Graph Inequalities (Resolver y representar desigualdades) — Isolate the variable, then show the complete solution set on a number line.
  • Solve (Resolver) — To find the number that makes it true.
  • Graph (Graficar) — To show answers on a number line with circles and shading.
  • Solution (Solución) — A number that makes the equation or inequality true.
  • Substitute (Sustituir) — To put a number in place of a letter.
  • Solution set (Conjunto solución) — All the numbers that make the inequality true.
4Watch out
  • 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.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    Final gate — describe the solution set. The vault rule is x > 7. What does the solution set mean?

    1. AAll numbers greater than 7, like 8, 9, 10, … (but NOT 7 itself)
    2. BOnly the number 7
    3. CAll numbers less than 7
    4. DEvery number, including 7
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    Solve: x − 4 < 11

    1. Ax < 15
    2. Bx < 7
    3. Cx > 15
    4. Dx = 15
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    Is x = 5 a solution to x + 4 > 12?

    1. ANo, because 5 + 4 = 9, and 9 is not greater than 12
    2. BYes, because 5 + 4 = 9
    3. CYes, because 5 > 4
    4. DNo, because 5 < 12
    ✏️ Workspace & Solution Steps
  3. 4 MULTIPLE CHOICE

    Clue 1: Which value is a solution of x > 7?

    1. A9
    2. B7
    3. C5
    4. D3
    ✏️ Workspace & Solution Steps
  4. 5 MULTIPLE CHOICE

    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
    ✏️ Workspace & Solution Steps
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It