Learn on PengiBig Ideas Math, Advanced 2Chapter 1: Equations

Section 1.1: Solving Simple Equations

In this Grade 7 lesson from Big Ideas Math Advanced 2, Chapter 1, students learn to solve simple equations using the Addition, Subtraction, Multiplication, and Division Properties of Equality. The lesson begins with inductive reasoning to discover that the angles of a triangle sum to 180 degrees, then applies that rule to write and solve one-step equations with integers, decimals, fractions, and pi. Students practice using inverse operations to isolate variables and check their solutions for accuracy.

Section 1

Solving with addition and subtraction

Property

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

Addition Property of Equality: For any numbers $a$ , $b$ , and $c$ , if $a = b$ , then $a + c = b + c$ .

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

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.

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Chapter 1: Equations

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Lesson 1Current
Section 1.1: Solving Simple Equations
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Lesson 2
Section 1.2: Solving Multi-Step Equations
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Lesson 3
Section 1.3: Solving Equations with Variables on Both Sides
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Lesson 4
Lesson 4: Rewriting Equations and Formulas
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Section 1

Solving with addition and subtraction

Property

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

Addition Property of Equality: For any numbers $a$ , $b$ , and $c$ , if $a = b$ , then $a + c = b + c$ .

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

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.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 1: Equations

Back to Big Ideas Math, Advanced 2

Lesson 1Current
Section 1.1: Solving Simple Equations
Learn Practice
Lesson 2
Section 1.2: Solving Multi-Step Equations
Learn Practice
Lesson 3
Section 1.3: Solving Equations with Variables on Both Sides
Learn Practice
Lesson 4
Lesson 4: Rewriting Equations and Formulas
Learn Practice

Overview

Lesson overview

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

Overview

Section 1

Solving with addition and subtraction

Property

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

Addition Property of Equality: For any numbers $a$ , $b$ , and $c$ , if $a = b$ , then $a + c = b + c$ .

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

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.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 1: Equations

Back to Big Ideas Math, Advanced 2

Lesson 1Current
Section 1.1: Solving Simple Equations
Learn Practice
Lesson 2
Section 1.2: Solving Multi-Step Equations
Learn Practice
Lesson 3
Section 1.3: Solving Equations with Variables on Both Sides
Learn Practice
Lesson 4
Lesson 4: Rewriting Equations and Formulas
Learn Practice

Section 1.1: Solving Simple Equations

Property

Property

Chapter 1: Equations

Section 1.1: Solving Simple Equations

Section 1.2: Solving Multi-Step Equations

Section 1.3: Solving Equations with Variables on Both Sides

Lesson 4: Rewriting Equations and Formulas

Lesson overview

Property

Property

Chapter 1: Equations

Section 1.1: Solving Simple Equations

Section 1.2: Solving Multi-Step Equations

Section 1.3: Solving Equations with Variables on Both Sides

Lesson 4: Rewriting Equations and Formulas

Section 1.1: Solving Simple Equations

Section 1.2: Solving Multi-Step Equations

Section 1.3: Solving Equations with Variables on Both Sides

Lesson 4: Rewriting Equations and Formulas