Unit 7 · Standard 6.EE.5

Solve and Graph Inequalities

Lesson 7-6

Name:Date:Class:

Key Vocabulary Level 1 support

Picture first, then the word, then a plain-language meaning. Say each word out loud.

x + 3 > 10 → subtract 3 → x > 7 — any number greater than 7 works

Solve

To find the number that makes it true.

x > 7: open circle at 7, shade right — shows all solutions at a glance

Graph

To show answers on a number line with circles and shading.

x = 8 is a solution to x > 7 because 8 > 7 is true; x = 5 is not because 5 > 7 is false

Solution

A number that makes the equation or inequality true.

Substitute x = 5 into x + 3 > 10: 5 + 3 = 8, and 8 > 10 is false, so x = 5 is not a solution

Substitute

To put a number in for the letter to check if it works.

Key Ideas & Notes

Detective Kim knows that the suspect withdrew more than $50 from an ATM.
The amount plus a $3 fee totaled more than $53.
She writes x + 3 > 53 and needs to solve for x, then graph the solution set to share with the bank.
How can she find and display all possible withdrawal amounts?
Solve each inequality using inverse operations, then graph the solution on the number line.

Think About It

What is the unknown in this situation?
What operation do you need to undo?
Will the answer be one number or many numbers?

My Notes

Guided Examples

Example 1

Solve: x + 6 > 14

Solution: Subtract 6 from both sides: x > 14 − 6 = 8. Graph: open circle at 8, shade right.

Answer: A. x > 8

Example 2

Solve: x − 9 ≤ 3

Solution: Add 9 to both sides: x ≤ 3 + 9 = 12. Graph: closed circle at 12, shade left.

Answer: A. x ≤ 12

Example 3

Solve: x + 10 ≥ 25

Solution: Subtract 10 from both sides: x ≥ 25 − 10 = 15. Graph: closed circle at 15, shade right.

Answer: A. x ≥ 15

Write About the Math The Writing Revolution

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

1. Kernel Sentence subject + verb

Model: Solve is to find the number that makes it true.Resolver es encontrar el número que la hace verdadera.

Write a kernel sentence about solve. Use a subject and a verb.Escribe una oración base sobre resolver. Usa un sujeto y un verbo.

2. Sentence Expansion because · but · so

Kernel: Solve matters in mathResolver importa en matemáticas

Expand the kernel three ways. Add a reason, a contrast, and a result.

becauseporque

Solve matters in math because ___.Resolver importa en matemáticas porque ___.

butpero

Solve matters in math, but ___.Resolver importa en matemáticas, pero ___.

soentonces

Solve matters in math, so ___.Resolver importa en matemáticas, entonces ___.

3. Sentence Types 4 ways to write a math idea

StatementAfirmación

Tell one true fact about solve.Di un hecho verdadero sobre solve.

Solve ___.

QuestionPregunta

Ask a question about solve.Haz una pregunta sobre solve.

How does ___ ?¿Cómo ___ ?

ExclamationExclamación

Show excitement about solve.Muestra entusiasmo sobre solve.

Wow, ___ !¡Guau, ___ !

CommandMandato

Tell a partner what to do with solve.Dile a un compañero qué hacer con solve.

First, ___ .Primero, ___ .

4. Explain Your Reasoning use a sentence starter

First I solved by ___.Primero resolví al ___.

Then I graphed ___.Luego grafiqué ___.

This keeps me within ___.Esto me mantiene dentro de ___.

Try It

Solve on your own. Check the answer key when you are done.

1. Solve: x − 4 < 11

x < 15
x < 7
x > 15
x = 15

Show your work:

2. Is x = 5 a solution to x + 4 > 12?

No, because 5 + 4 = 9, and 9 is not greater than 12
Yes, because 5 + 4 = 9
Yes, because 5 > 4
No, because 5 < 12

Show your work:

Stretch Your Thinking Level 2 enrichment

Challenge task — explain your reasoning in full sentences.

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.

Sentence starter: Inequality: 37 + r ≤ ___. Solving: r ≤ ___ − 37 = ___. Graph: ___ circle at ___, shade ___. Three possible values: ___.

Show your work:

Reflect — Exit Ticket

Solve and describe the graph: x + 5 < 11

x < 6; open circle at 6, shade left
x < 16; open circle at 16, shade left
x ≤ 6; closed circle at 6, shade left
x > 6; open circle at 6, shade right

Your answer:

Answer Key & Teacher Guide

Try It 1: A. x < 15 — Add 4 to both sides: x < 11 + 4 = 15. Graph: open circle at 15, shade left.
Try It 2: A. No, because 5 + 4 = 9, and 9 is not greater than 12 — Substitute: 5 + 4 = 9. Since 9 > 12 is false, x = 5 is NOT a solution.
Exit Ticket: A. x < 6; open circle at 6, shade left — Subtract 5 from both sides: x < 11 − 5 = 6. Open circle at 6 (not included), shade left. ✓

Writing (TWR) — what to look for

Kernel sentence: A complete sentence needs a subject and a verb. Example: Solve is to find the number that makes it true.
Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).