Solving Equations with Variables on Both Sides

This video tutorial covers solving equations with variables on both sides. It explains the parts of an equation, including variables, coefficients, and constants. The tutorial walks through three steps to solve such equations: distributing and combining like terms, collecting variable and constant terms, and isolating the variable. Several example problems are solved, and a real-world application is discussed to reinforce the concepts. The video concludes with a summary of the key points.

What represents an unknown value in an equation?

• Constant

• Equation

• Coefficient

• Variable

What is a coefficient in an equation?

• A number multiplied by the variable

• A fixed number without a variable

• The solution to the equation

• The operation between terms

What is the first step in solving equations with variables on both sides?

• Isolate the variable

• Combine like terms and distribute

• Collect variable terms on one side

• Divide both sides by the coefficient

What does distributing involve in solving equations?

• Adding variables

• Multiplying terms inside parentheses

• Isolating constants

• Subtracting coefficients

What operation is used to collect variable terms on one side?

• Distribution

• Multiplication

• Addition

• Inverse operations

How do you isolate the variable in an equation?

• Add coefficients

• Combine like terms

• Use inverse operations

• Subtract constants

How do you determine which side to collect variable terms on?

• The side with the larger coefficient

• The side with fewer terms

• The right side always

• The left side always

What is the purpose of adding or subtracting the same term on both sides of an equation?

• To simplify the equation

• To combine like terms

• To eliminate the variable

• To balance the equation

In the context of the video, what does 'undoing multiplication' refer to?

• Multiplying both sides by the variable

• Dividing both sides by the coefficient

• Adding a constant

• Subtracting the coefficient

For what number of months would it cost the same to be a member at either gym, according to the real-world problem solved?

• 7 months

• 8 months

• 6 months

• 5 months