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Examples, solutions, videos, and worksheets to help Grade 7 and Grade 8 learn how to transform equations into simpler forms using the distributive property and solve the equations. Learn that not every linear equation has a solution.

Transforming and solving equations using the distributive property involves applying the property to simplify the equation, then solving it as you would any linear equation. Below is a detailed explanation of how to do this.

Steps to Transform and Solve Equations Using the Distributive Property

- Apply the Distributive Property

The distributive property states:

a(b+c)=ab+ac

When you have an expression like a(b+c), multiply the term outside the parentheses by each term inside the parentheses. - Combine Like Terms (if needed)

After distributing, look for any like terms on each side of the equation and combine them to simplify the equation. - Move All Variable Terms to One Side

Use addition or subtraction to move all terms containing the variable to one side of the equation. - Move All Constant Terms to the Other Side

Use addition or subtraction to move all constant terms to the other side of the equation. - Solve for the Variable

Use multiplication or division to isolate the variable and solve the equation. - Check Your Solution

Substitute the solution back into the original equation to verify that it satisfies the equation.

A linear equation has no solution when, after simplifying, you end up with a statement that is always false, like 5=0. This usually happens when the equation involves two expressions that cannot be equal no matter what value of the variable you use.

Have a look at this video if you need to review how to solve linear equations using distribution.

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Solve Linear Equation, Distributive

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