Variables on Both Sides Word Problems

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

What does it mean to solve an equation with variables on both sides?

Back

It means to find the value of the variable that makes both sides of the equation equal by isolating the variable.

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 is the first step in solving the equation 7w + 5 = 3w - 15?

Back

The first step is to get all terms containing the variable on one side and constant terms on the other side.

Front

What is the solution to the equation 7w + 5 = 3w - 15?

Back

The solution is w = -5.

Front

How do you set up an equation for a word problem involving costs?

Back

Identify the fixed costs and variable costs, then create an equation that represents the total cost for each option.

Front

What equation represents the cost of going to the Frederick County Fair?

Back

The equation is C = 15 + 2.5x, where C is the total cost and x is the number of rides.

Front

What is the equation to find when both fairs cost the same?

Back

The equation is 15 + 2.5x = 10 + 3x.

Front

How do you determine the number of miles for equal rental costs?

Back

Set the total cost equations for both rental agencies equal to each other and solve for the number of miles.

Front

What is the cost equation for the first rental car agency?

Back

The equation is C = 30 + 0.15m, where C is the total cost and m is the number of miles.