Graph Inequalities

6.AT.11 · Unit 7 · Lesson 5

Name   Period

Objectives / Objetivos

Content Objective: I can graph the solutions of an inequality on a number line.

Language Objective: I can explain my graph using the words number line, open circle, closed circle, and solution set.

Key Idea / Idea clave

Closed circle for ≤ or ≥ (included), open circle for < or > (not included); shade right for greater, left for less.

I Notice / Observo

  • What does 'no earlier than 2:00 PM' mean about the time?
  • Should 2:00 PM itself be included?

I Wonder / Me pregunto

  • What would the graph look like if the suspect arrived before 2:00 PM?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Number line
Recta numérica		A straight line where numbers are placed in order; numbers get smaller to the left and larger to the right.
Una recta donde los números se colocan en orden; los números son menores a la izquierda y mayores a la derecha.
Open circle
Círculo abierto		An empty circle showing a number is NOT included.
Un círculo vacío que muestra que un número NO está incluido.
Closed circle
Círculo cerrado		A filled-in circle showing a number IS included.
Un círculo relleno que muestra que un número SÍ está incluido.
Solution set
Conjunto solución		All the numbers that make the inequality true.
Todos los números que hacen verdadera la desigualdad.
Inequality
Desigualdad		A math sentence comparing two amounts with <, >, ≤, or ≥.
Una oración matemática que compara dos cantidades con <, >, ≤ o ≥.
Boundary point
Punto límite		The number on the number line where the solution set starts.
El número en la recta numérica donde comienza el conjunto solución.

Practice Preview / Vista previa de práctica

  1. Which graph represents x < 5?
    1. Open circle at 5, shaded left
    2. Closed circle at 5, shaded left
    3. Open circle at 5, shaded right
    4. Closed circle at 5, shaded right
  2. Match each inequality to its graph description
    • → ___
    • → ___
    • → ___
  3. Read the graph description and write the inequality it represents. Then graph it.
  4. Find the Graphing Error
    1. Step 1: Inequality — x > 6
    2. Step 2: Circle type — Closed circle at 6
    3. Step 3: Shade direction — Shade right
    4. Step 4: Graph — Closed circle at 6, shaded right

    Which step has the mistake? Explain it and write the correct work.

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: