Solve and Graph Inequalities

6.AT.8 · Unit 7 · Lesson 6

Name   Period

Objectives / Objetivos

Content Objective: I can solve an inequality and graph its solution set on a number line.

Language Objective: I can explain my work using the words solve, graph, solution, and substitute.

Key Idea / Idea clave

Solve with inverse operations, then graph the solution set: open circle for < or >, closed for ≤ or ≥.

I Notice / Observo

  • What is the unknown in this situation?
  • What operation do you need to undo?

I Wonder / Me pregunto

  • What if the total was at most $53 instead of more than $53?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Solve
Resolver		To find the number that makes it true.
Encontrar el número que la hace verdadera.
Graph
Graficar		To show answers on a number line with circles and shading.
Mostrar respuestas en una recta numérica con círculos y sombreado.
Solution
Solución		A number that makes the equation or inequality true.
Un número que hace verdadera la ecuación o desigualdad.
Substitute
Sustituir		To put a number in place of a letter.
Poner un número en lugar de una letra.
Solution set
Conjunto solución		All the numbers that make the inequality true.
Todos los números que hacen verdadera la desigualdad.
Inverse operation
Operación inversa		Two math actions that undo each other, like × and ÷.
Dos operaciones que se deshacen entre sí, como × y ÷.

Practice Preview / Vista previa de práctica

  1. Solve: x + 6 > 14
    1. x > 8
    2. x > 20
    3. x < 8
    4. x = 8
  2. Solve each inequality, describe the inverse operation, and describe the graph.
  3. Is x = 5 a solution to x + 4 > 12?
    1. No, because 5 + 4 = 9, and 9 is not greater than 12
    2. Yes, because 5 + 4 = 9
    3. Yes, because 5 > 4
    4. No, because 5 < 12
  4. Find the Solving Error
    1. Step 1: Inequality — x − 8 ≥ 15
    2. Step 2: Inverse operation — Subtract 8 from both sides
    3. Step 3: Simplify — x ≥ 7
    4. Step 4: Graph — Closed circle at 7, shade 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: