Learn on PengiBig Ideas Math, Course 2Chapter 3: Expressions and Equations

Lesson 3: Solving Equations Using Addition or Subtraction

Grade 7 students learn how to solve one-variable addition and subtraction equations by applying the Addition Property of Equality and Subtraction Property of Equality to produce equivalent equations. The lesson uses algebra tiles to model isolating the variable through zero pairs, then connects that hands-on method to solving equations using inverse operations. This is covered in Lesson 3.3 of Chapter 3: Expressions and Equations in Big Ideas Math, Course 2, aligned to standard MAFS.7.EE.2.4a.

Section 1

Subtraction and Addition Properties of Equality

Property

Subtraction Property of Equality
For all real numbers $a$ , $b$ , and $c$ , if $a = b$ , then $a - c = b - c$ .

Addition Property of Equality
For all real numbers $a$ , $b$ , and $c$ , if $a = b$ , then $a + c = b + c$ .
When you add or subtract the same quantity from both sides of an equation, you still have equality.

Examples

To solve $p - 7 = 12$ , we use the Addition Property. Add 7 to both sides: $p - 7 + 7 = 12 + 7$ , which simplifies to $p = 19$ .

Section 2

Isolating the variable

Property

To solve an equation, we isolate the variable. The process is:

Ask yourself: Which operation has been performed on the variable?
Perform the opposite operation on both sides of the equation to maintain balance.
Check your solution by substituting it into the original equation.

Examples

To solve $x - 5 = 12$ , we undo the subtraction by adding 5 to both sides: $(x - 5) + 5 = 12 + 5$ , which simplifies to $x = 17$ .

To solve $y + 9 = 20$ , we undo the addition by subtracting 9 from both sides: $(y + 9) - 9 = 20 - 9$ , which simplifies to $y = 11$ .

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Subtraction and Addition Properties of Equality

Property

Subtraction Property of Equality
For all real numbers $a$ , $b$ , and $c$ , if $a = b$ , then $a - c = b - c$ .

Examples

To solve $p - 7 = 12$ , we use the Addition Property. Add 7 to both sides: $p - 7 + 7 = 12 + 7$ , which simplifies to $p = 19$ .

Section 2

Isolating the variable

Property

To solve an equation, we isolate the variable. The process is:

Ask yourself: Which operation has been performed on the variable?
Perform the opposite operation on both sides of the equation to maintain balance.
Check your solution by substituting it into the original equation.

Examples

To solve $x - 5 = 12$ , we undo the subtraction by adding 5 to both sides: $(x - 5) + 5 = 12 + 5$ , which simplifies to $x = 17$ .

To solve $y + 9 = 20$ , we undo the addition by subtracting 9 from both sides: $(y + 9) - 9 = 20 - 9$ , which simplifies to $y = 11$ .

Overview

Lesson overview

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

Overview

Section 1

Subtraction and Addition Properties of Equality

Property

Subtraction Property of Equality
For all real numbers $a$ , $b$ , and $c$ , if $a = b$ , then $a - c = b - c$ .

Examples

To solve $p - 7 = 12$ , we use the Addition Property. Add 7 to both sides: $p - 7 + 7 = 12 + 7$ , which simplifies to $p = 19$ .

Section 2

Isolating the variable

Property

To solve an equation, we isolate the variable. The process is:

Ask yourself: Which operation has been performed on the variable?
Perform the opposite operation on both sides of the equation to maintain balance.
Check your solution by substituting it into the original equation.

Examples

To solve $x - 5 = 12$ , we undo the subtraction by adding 5 to both sides: $(x - 5) + 5 = 12 + 5$ , which simplifies to $x = 17$ .

To solve $y + 9 = 20$ , we undo the addition by subtracting 9 from both sides: $(y + 9) - 9 = 20 - 9$ , which simplifies to $y = 11$ .