Linear Equations and Solutions

The video tutorial explains how to solve linear equations with variables on both sides. It begins with an introduction to the concept, followed by setting up an example equation. The tutorial then demonstrates the process of solving the equation by eliminating fractions and simplifying it to isolate the variable. Finally, it verifies the solution by substituting the value back into the original equation, ensuring the solution is correct.

What is the first step in solving a linear equation with variables on both sides?

• Identify the variables on both sides

• Subtract the same number from both sides

• Multiply both sides by zero

• Add the same number to both sides

In the equation 2y/3 + 1 = 7y/15 + 3, what is the LCM of the denominators?

• 21

• 7

• 15

• 3

Why do we multiply both sides of the equation by the LCM?

• To make the equation longer

• To make the equation more complex

• To eliminate fractions

• To add more variables

What is the purpose of finding the LCM of the denominators?

• To make the equation more complex

• To add more variables

• To eliminate fractions

• To make the equation longer

What happens when you multiply 15 by 2y/3?

• You get 15y

• You get 45y

• You get 30y

• You get 10y

What is the result of multiplying 15 by 7/15y?

• 15y

• 45y

• 7y

• 30y

What is the purpose of subtracting 7y from both sides of the equation?

• To add more variables

• To eliminate the variable

• To isolate the variable on one side

• To make the equation more complex

What is the purpose of subtracting 7y from both sides of the equation?

• To isolate the variable on one side

• To eliminate the variable

• To make the equation more complex

• To add more variables

After subtracting 15 from both sides, what does the equation become?

• 3y = 15

• 3y = 45

• 3y = 30

• 3y = 60

What is the result of subtracting 15 from both sides of the equation 3y = 45?

• 3y = 30

• 3y = 15

• 3y = 60

• 3y = 45