Learn on PengiPengi Math (Grade 7)Chapter 6: Equations and Inequalities

Lesson 1: Solving Two-Step Equations

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

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

Solving with multiplication and division

Property

The Division Property of Equality: For any numbers $a$ , $b$ , and $c$ , and $c \neq 0$ , if $a = b$ , then $\frac{a}{c} = \frac{b}{c}$ .

The Multiplication Property of Equality: For any numbers $a$ , $b$ , and $c$ , if $a = b$ , then $ac = bc$ .

Use these properties to isolate the variable by performing the inverse operation on both sides of the equation.

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

Solving with multiplication and division

Property

The Division Property of Equality: For any numbers $a$ , $b$ , and $c$ , and $c \neq 0$ , if $a = b$ , then $\frac{a}{c} = \frac{b}{c}$ .

The Multiplication Property of Equality: For any numbers $a$ , $b$ , and $c$ , if $a = b$ , then $ac = bc$ .

Use these properties to isolate the variable by performing the inverse operation on both sides of the equation.

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

Solving with multiplication and division

Property

The Division Property of Equality: For any numbers $a$ , $b$ , and $c$ , and $c \neq 0$ , if $a = b$ , then $\frac{a}{c} = \frac{b}{c}$ .

The Multiplication Property of Equality: For any numbers $a$ , $b$ , and $c$ , if $a = b$ , then $ac = bc$ .

Use these properties to isolate the variable by performing the inverse operation on both sides of the equation.