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

8.6 · Part II

Second Practice Form · Independent Application and Spiral Review

Solve and Graph Inequalities · Solve

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 8.6 · Part II
1Solving & Graphing One-Step Inequalities
2The Structural Procedure
  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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

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

    1. AAn open circle at 15 with shading to the right
    2. BA closed circle at 15 with shading to the right
    3. CAn open circle at 3 with shading to the right
    4. DAn open circle at 15 with shading to the left
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Solve: x + 6 > 14

    1. Ax > 8
    2. Bx > 20
    3. Cx < 8
    4. Dx = 8
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Solve: x − 9 ≤ 3

    1. Ax ≤ 12
    2. Bx ≤ 6
    3. Cx ≥ 12
    4. Dx = 12
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Solve: x + 10 ≥ 25

    1. Ax ≥ 15
    2. Bx ≥ 35
    3. Cx ≤ 15
    4. Dx = 15
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 OPEN RESPONSE

    A detective has a budget of at most $100 for supplies. She already spent $37 on gloves. Write an inequality for the remaining amount r she can spend, solve it, graph it, and name three possible values for r.

    ✏️ Mathematical Justification & Response
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

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

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It