Word problems: variables on both sides

Front

What is a variable in an equation?

Back

A variable is a symbol, often represented by a letter, that stands for an unknown value in an equation.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What does it mean to have variables on both sides of an equation?

Back

It means that the variable appears on both sides of the equation, requiring manipulation to solve for the variable.

Front

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

Back

The first step is to simplify both sides of the equation, if necessary, and then move all terms involving the variable to one side.

Front

How do you solve the equation 10x + 9 = 4x - 9?

Back

Subtract 4x from both sides to get 6x + 9 = -9, then subtract 9 from both sides to get 6x = -18, and finally divide by 6 to find x = -3.

Front

What is a word problem in mathematics?

Back

A word problem is a mathematical question presented in the form of a narrative, requiring interpretation and translation into an equation.

Front

How do you set up an equation from a word problem?

Back

Identify the variables, constants, and relationships described in the problem, then translate these into a mathematical equation.

Front

What is the significance of the membership card in Juan's gym problem?

Back

The membership card represents a fixed cost that affects the total cost depending on the number of visits to the gym.

Front

How do you determine when two costs are equal in a word problem?

Back

Set the equations representing the two costs equal to each other and solve for the variable.

Front

What is the equation to find when the cost of Xbox One and Playstation 4 games are equal?

Back

The equation is 150 + 24x = 180 + 20x, where x is the number of games.