Learn on PengiBig Ideas Math, Course 1Chapter 7: Equations and Inequalities

Lesson 2: Solving Equations Using Addition or Subtraction

In this Grade 6 lesson from Big Ideas Math Course 1, Chapter 7, students learn to solve one-variable equations using the Addition Property of Equality and the Subtraction Property of Equality by applying inverse operations to isolate the variable. Students also practice checking solutions through substitution to verify whether a given value makes an equation true. The lesson aligns with Common Core standards 6.EE.5 and 6.EE.7 and includes real-life problem-solving applications.

Section 1

Determining Solutions by Substitution

Property

A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.
To determine whether a number is a solution to an equation:

Step 1. Substitute the number for the variable in the equation.
Step 2. Simplify the expressions on both sides of the equation.
Step 3. Determine whether the resulting equation is true.

If it is true, the number is a solution.
If it is not true, the number is not a solution.

Examples

Is $x=5$ a solution to the equation $3x - 5 = 10$ ? We substitute $3(5) - 5 = 15 - 5 = 10$ . Since $10 = 10$ , it is a solution.
Is $y=-2$ a solution to the equation $4y + 9 = 2y$ ? We substitute $4(-2) + 9 = -8 + 9 = 1$ on the left, and $2(-2) = -4$ on the right. Since $1 \neq -4$ , it is not a solution.
Is $a = \frac{1}{3}$ a solution to the equation $9a + 2 = 5$ ? We substitute $9(\frac{1}{3}) + 2 = 3 + 2 = 5$ . Since $5=5$ , it is a solution.

Section 2

Inverse Operations: Addition and Subtraction

Property

Addition and subtraction are inverse operations, which means they "undo" each other. For any number $n$ :

x + n - n = x

x - n + n = x

Examples

Section 3

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.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Determining Solutions by Substitution

Property

A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.
To determine whether a number is a solution to an equation:

Step 1. Substitute the number for the variable in the equation.
Step 2. Simplify the expressions on both sides of the equation.
Step 3. Determine whether the resulting equation is true.

If it is true, the number is a solution.
If it is not true, the number is not a solution.

Examples

Is $x=5$ a solution to the equation $3x - 5 = 10$ ? We substitute $3(5) - 5 = 15 - 5 = 10$ . Since $10 = 10$ , it is a solution.
Is $y=-2$ a solution to the equation $4y + 9 = 2y$ ? We substitute $4(-2) + 9 = -8 + 9 = 1$ on the left, and $2(-2) = -4$ on the right. Since $1 \neq -4$ , it is not a solution.
Is $a = \frac{1}{3}$ a solution to the equation $9a + 2 = 5$ ? We substitute $9(\frac{1}{3}) + 2 = 3 + 2 = 5$ . Since $5=5$ , it is a solution.

Section 2

Inverse Operations: Addition and Subtraction

Property

Addition and subtraction are inverse operations, which means they "undo" each other. For any number $n$ :

x + n - n = x

x - n + n = x

Examples

Section 3

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.

Overview

Lesson overview

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

Overview

Section 1

Determining Solutions by Substitution

Property

A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.
To determine whether a number is a solution to an equation:

Step 1. Substitute the number for the variable in the equation.
Step 2. Simplify the expressions on both sides of the equation.
Step 3. Determine whether the resulting equation is true.

If it is true, the number is a solution.
If it is not true, the number is not a solution.

Examples

Is $x=5$ a solution to the equation $3x - 5 = 10$ ? We substitute $3(5) - 5 = 15 - 5 = 10$ . Since $10 = 10$ , it is a solution.
Is $y=-2$ a solution to the equation $4y + 9 = 2y$ ? We substitute $4(-2) + 9 = -8 + 9 = 1$ on the left, and $2(-2) = -4$ on the right. Since $1 \neq -4$ , it is not a solution.
Is $a = \frac{1}{3}$ a solution to the equation $9a + 2 = 5$ ? We substitute $9(\frac{1}{3}) + 2 = 3 + 2 = 5$ . Since $5=5$ , it is a solution.

Section 2

Inverse Operations: Addition and Subtraction

Property

Addition and subtraction are inverse operations, which means they "undo" each other. For any number $n$ :

x + n - n = x

x - n + n = x

Examples

Section 3

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.