Learn on PengiBig Ideas Math, Course 2Chapter 4: Inequalities

Lesson 2: Solving Inequalities Using Addition or Subtraction

In this Grade 7 lesson from Big Ideas Math, Course 2, Chapter 4, students learn how to solve one-variable inequalities using the Addition Property of Inequality and the Subtraction Property of Inequality. Students practice isolating the variable by applying inverse operations, then graphing the solution set on a number line using open and closed circles. Real-life contexts, such as temperature comparisons and age restrictions, are used to reinforce writing and solving inequalities of the form x + c < b and x − c ≥ b.

Section 1

Addition and Subtraction Properties of Inequality

Property

Subtraction Property of Inequality
For any numbers $a$ , $b$ , and $c$ ,
if $a < b$ , then $a - c b$ , then $a - c > b - c$ .

Addition Property of Inequality
For any numbers $a$ , $b$ , and $c$ ,
if $a < b$ , then $a + c b$ , then $a + c > b + c$ .

Examples

To solve $x + 7 \leq 15$ , subtract 7 from both sides. This gives $x \leq 8$ . The solution is all numbers less than or equal to 8, or $(-\infty, 8]$ .

Section 2

Common Errors in Inequality Solving and Graphing

Property

Common error patterns: Flipping inequality symbols incorrectly when no multiplication/division by negatives occurs, using open circles for $\leq$ or $\geq$ inequalities, using closed circles for $<$ or $>$ inequalities, and misreading inequality direction when graphing solutions.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Addition and Subtraction Properties of Inequality

Property

Subtraction Property of Inequality
For any numbers $a$ , $b$ , and $c$ ,
if $a < b$ , then $a - c b$ , then $a - c > b - c$ .

Addition Property of Inequality
For any numbers $a$ , $b$ , and $c$ ,
if $a < b$ , then $a + c b$ , then $a + c > b + c$ .

Examples

To solve $x + 7 \leq 15$ , subtract 7 from both sides. This gives $x \leq 8$ . The solution is all numbers less than or equal to 8, or $(-\infty, 8]$ .

Section 2

Common Errors in Inequality Solving and Graphing

Property

Examples

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Addition and Subtraction Properties of Inequality

Property

Subtraction Property of Inequality
For any numbers $a$ , $b$ , and $c$ ,
if $a < b$ , then $a - c b$ , then $a - c > b - c$ .

Addition Property of Inequality
For any numbers $a$ , $b$ , and $c$ ,
if $a < b$ , then $a + c b$ , then $a + c > b + c$ .

Examples

To solve $x + 7 \leq 15$ , subtract 7 from both sides. This gives $x \leq 8$ . The solution is all numbers less than or equal to 8, or $(-\infty, 8]$ .

Section 2

Common Errors in Inequality Solving and Graphing