Understand Inequalities and Their Solutions
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
Graphing Inequalities on the Number Line. 1. Draw the boundary circle at the given constant number. 2. Open Circle (○) for < or > (boundary value is not included in solution set). 3. Closed Circle (●) for ≤ or ≥ (boundary value is included). Shade right for >, left for <
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 / Término | Definition / Definición |
|---|---|
| Graph Inequalities Representar desigualdades en una recta numérica | Show every solution to an inequality on a number line with a boundary point and an arrow. Mostrar cada solución de una desigualdad en una recta numérica con un punto límite y una flecha. |
| 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 that compares two sides with <, >, ≤, or ≥. Una oración matemática que compara dos lados con <, >, ≤ o ≥. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. Which graph represents x < 5?
- A Open circle at 5, shaded left
- B Closed circle at 5, shaded left
- C Open circle at 5, shaded right
- D Closed circle at 5, shaded right
Answer:
2. Match each inequality to its graph description
Write the letter of the matching item in the blank.
| 1. | x > 10 | A. | Open circle at 10, shaded right | |
| 2. | x ≤ 6 | B. | Open circle at 9, shaded left | |
| 3. | x ≥ 1 | C. | Closed circle at 6, shaded left | |
| 4. | x < 9 | D. | Closed circle at 1, shaded right |
3. Read the graph description and write the inequality it represents. Then graph it.
1. x ≥ 5
2. x < 3
4. Find the Graphing Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: