Solving Equations with Variables on Both Sides

Front

What is the general form of an equation with variables on both sides?

Back

An equation with variables on both sides typically has the form: ax + b = cx + d, where a, b, c, and d are constants.

Front

How do you isolate a variable in an equation with variables on both sides?

Back

To isolate a variable, you can move all terms involving the variable to one side of the equation and constant terms to the other side, then simplify.

Front

What is the first step in solving the equation 12 + 5x = 3x + 18?

Back

The first step is to move all terms involving x to one side and constant terms to the other side, which can be done by subtracting 3x from both sides.

Front

What does it mean for two services to have the same total cost?

Back

It means that the equations representing the total costs of both services are equal for a certain number of hours.

Front

How do you determine which service is more economical based on cost?

Back

You can compare the total costs of each service for a given number of hours and choose the one with the lower cost.

Front

What is the solution to the equation 7x = 3x + 24?

Back

The solution is x = 6.

Front

How do you check if your solution to an equation is correct?

Back

You can substitute the solution back into the original equation to see if both sides are equal.

Front

What is the solution to the equation f - 4 = 6f + 26?

Back

The solution is f = -6.

Front

What is the process for solving the equation 100 - 6x = 160 - 10x?

Back

First, move all x terms to one side and constant terms to the other side, then solve for x.

Front

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

Back

It means that the variable appears in expressions on both sides of the equality sign.