Write and Solve Equations with Variables on Both Sides

Front

What is an equation with variables on both sides?

Back

An equation that contains variables on both the left and right sides, requiring manipulation to isolate the variable.

Front

How do you solve an equation with variables on both sides?

Back

1. Move all terms involving the variable to one side of the equation. 2. Move constant terms to the other side. 3. Simplify and solve for the variable.

Front

What is the first step in solving the equation 15 + 2.5x = 10 + 3x?

Back

Subtract 2.5x from both sides to get 15 = 10 + 0.5x.

Front

In the context of the quiz, what does 'equal value' mean?

Back

It refers to the point at which two different costs or values become the same.

Front

What does it mean to write an equation to represent a situation?

Back

It means to create a mathematical expression that models the relationships and conditions described in a real-world scenario.

Front

How can you determine the number of games needed for two locations to cost the same?

Back

By setting up an equation that equates the total costs of both locations and solving for the number of games.

Front

What is the significance of the coefficients in an equation like 2.50x = 15 + x?

Back

The coefficients represent the cost per ride or game, which helps in determining the total cost based on the number of rides or games.

Front

What does it mean when one person is gaining followers and another is losing followers?

Back

It indicates a dynamic situation where the rates of change (gaining vs. losing) can be modeled with an equation to find when their follower counts will be equal.

Front

How do you interpret the solution to an equation in a real-world context?

Back

The solution represents the specific value (e.g., number of rides, games, weeks) at which two scenarios become equal.

Front

What is the role of constants in equations like 15 + 2.5x = 10 + 3x?

Back

Constants represent fixed values that do not change, such as entry fees or initial amounts.