Lesson 5.4 Expressions & Equations

# Solve One- and Two-Step Inequalities

#### Materials

• CCB Mathematics pages 150 - 155

#### Standards

• MP.8

• Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

#### Objectives

• Translate verbal statements into inequalities

• Solve one-step inequalities

• Solve two-step inequalities

#### Key Concept

• Use inverse operations to solve one- and two-step inequalities.

#### Vocabulary

Tier 2 InfiniteReverse Inequality

## Before Lesson

To determine student readiness for this lesson, have them demonstrate their ability to solve 1- and 2-step equations. For example: x+5=9, x-10=2, 2x+35=115, x/8-1=2.

## Background

Tell students that solving one- and two-step inequalities is similar to solving one- and two-step equations. They both use inverse operations and the inverse order of operations. The one difference is when you multiply or divide by a negative number. Explain that equations are relationships showing that two expressions are equal, and inequalities compare expressions that may or may not be equal. Have students think of unequal relationships in real-life situations.

## Guided Practice

• Translate Verbal Statements into Inequalities
• Solve One-Step inequalities
• Solve Two-Step Inequalities

## Core Skill

Solve Inequalities: Allow students time to read the text. Have students write the rule for multiplying and dividing in their notebook. Explain that it is usually simplest to just memorize the rule. Have students solve the problems at the bottom of the sidebar and compare the solution sets.

Evaluate Reasoning: Have students read the sidebar. Explain to students that if they forget to flip the inequality symbol when they check their answer, the inequality will not be true. Explain that like in the story, this is something to look for when looking for a mistake. Emphasize how important it is to check the solution set, as this is one type of error that can be caught.

## Extension

Restate Examples: Invite students to select any example from the lesson to explain in their own words. Invite them to have other students ask questions. Assist them, if necessary, in answering those questions. Encourage discussion of concepts or processes that seem to cause confusion.

Assess Costs with Inequalities: Have students imagine they are taking a vacation. Their vacation budget is \$7,000. Have them write an inequality that includes the price of a hotel per night, cost of a rental car per day, and an estimate of food expenses per day. Have them use the inequality to decide how many days long their vacation can be. Encourage students to choose a variety of destinations, organizing all of the information and results.