Writing Equations with Variables on Both Sides

Front

What is an equation with variables on both sides?

Back

An equation that contains variables on both sides of the equal sign, requiring manipulation to solve for the variable.

Front

How do you represent a situation with an equation?

Back

Identify the quantities involved, assign variables, and create an equation that reflects the relationships between those quantities.

Front

Write an equation for: Peter and his friends can pay $2.00 for rentals plus $7.50 per game, while another location costs $8.00 for rentals plus $6.00 per game.

Back

2 + 7.50x = 8 + 6x

Front

Write an equation for: Shelby has $155 in savings, saving $10 each week, while George has $230, spending $15 each week.

Back

155 + 10x = 230 - 15x

Front

What does the equation 8 + 4x = 12 + 3x represent?

Back

It represents a situation where two growing quantities are equal, such as players on two teams.

Front

Write an equation for: John bought a car radio for $120 and speakers for $25 each, while Joe bought a radio for $45. How much did they spend?

Back

120 + 25x = 45x

Front

Write an equation for: Celebrity A has 400 followers gaining 75 each day, while Celebrity B has 1,000 followers losing 25 each day.

Back

400 + 75x = 1,000 - 25x

Front

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

Back

Combine like terms and isolate the variable on one side of the equation.

Front

What does it mean to isolate a variable in an equation?

Back

To manipulate the equation so that the variable is alone on one side, making it easier to solve.

Front

What is a common mistake when writing equations for word problems?

Back

Misinterpreting the relationships between quantities or incorrectly assigning variables.