Solving Equations with Distributive Property

This page continues with a second example problem, demonstrating how to apply the distributive property in a more complex equation.

Problem 2: 7 - 1(2a + 3) = 12

Step 1: Distribute -1

• Multiply -1 by each term inside the parentheses: 7 - 2a - 3 = 12

Step 2: Combine like terms

• Simplify the left side of the equation: 4 - 2a = 12

Step 3: Remove the constant

• Subtract 4 from both sides: -2a = 8

Step 4: Isolate the variable

• Divide both sides by -2: a = -4

Step 5: Solved

• The solution is a = -4

Example: In the problem 7 - 1(2a + 3) = 12, we distribute -1 to both 2a and 3, resulting in 7 - 2a - 3 = 12.

Highlight: This problem demonstrates how to do distributive property with variables on both sides of the equation.

This example showcases a more advanced application of the distributive property with variables and exponents, which is typical in 6th Grade Distributive Property Worksheet PDF exercises and Khan Academy distributive property with variables lessons.

Distributive Property with Variables

The distributive property is a crucial concept in algebra that involves multiplying a number outside parentheses by each term inside. This page introduces the concept and provides a step-by-step solution for the first example problem.

Definition: The distributive property is the multiplication of two numbers in parentheses by an outside number.

Problem 1: 4(x-3) = 20

Step 1: Distribute 4

• Multiply 4 by each term inside the parentheses: 4x - 12 = 20

Step 2: Remove the constant

• Add 12 to both sides of the equation: 4x = 32

Step 3: Isolate the variable

• Divide both sides by 4: x = 8

Step 4: Solved

• The solution is x = 8

Example: In the problem 4(x-3) = 20, we distribute 4 to both x and -3, resulting in 4x - 12 = 20.

Highlight: The distributive property with variables is a fundamental skill in solving equations with the distributive property.

This example demonstrates how to apply the distributive property with variables to solve an equation step by step, which is essential for middle school math distributive property practice.