Solve and Graph Inequalities
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
Solving & Graphing One-Step Inequalities. 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
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 / Término | Definition / Definición |
|---|---|
| Solve and Graph Inequalities Resolver y representar desigualdades | Isolate the variable, then show the complete solution set on a number line. Aislar la variable y luego mostrar el conjunto completo de soluciones en una recta numérica. |
| 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. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. Solve: x + 6 > 14
- A x > 8
- B x < 8
- C x = 8
- D x > 20
Answer:
2. Solve each inequality, describe the inverse operation, and describe the graph.
Complete each empty cell. Show your reasoning below.
| Inequality | Inverse Operation | Solution | Graph Description |
|---|---|---|---|
| x + 11 ≥ 20 | |||
| x − 3 < 7 | |||
| x + 8 ≤ 20 |
3. Is x = 5 a solution to x + 4 > 12?
- A No, because 5 + 4 = 9, and 9 is not greater than 12
- B Yes, because 5 + 4 = 9
- C Yes, because 5 > 4
- D No, because 5 < 12
Answer:
4. Find the Solving Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: