7.1b Writing/ Solving Equations with Variables on Both Sides

Front

What is an equation with variables on both sides?

Back

An equation that has 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 variable terms to one side of the equation. 2. Move constant terms to the other side. 3. Combine like terms and isolate the variable.

Front

What is the first step in solving the equation 30 + 0.15m = 36 + 0.10m?

Back

Subtract 0.10m from both sides to get 30 + 0.05m = 36.

Front

If a rental car costs $30 per day plus $0.15 per mile, how would you express the total cost as an equation?

Back

Total Cost = 30 + 0.15m, where m is the number of miles driven.

Front

What does it mean for two rental agencies to cost the same amount?

Back

It means that the total costs from both agencies can be set equal to each other to find the number of miles or hours.

Front

In the problem about Joe and Josh, what are the variables?

Back

Let J be the amount of money Joe has after w weeks, and K be the amount of money Josh has after w weeks.

Front

How do you set up an equation to find when Joe and Josh have the same amount of money?

Back

Set the equations J = 14 + 10w and K = 26 + 7w equal to each other.

Front

What is the solution to the equation 14 + 10w = 26 + 7w?

Back

w = 4 weeks.

Front

How do you determine which video club is a better deal?

Back

Calculate the total cost for each club based on the number of videos rented and compare the totals.

Front

What is the total cost for renting 6 videos from club A?

Back

Total Cost = 25 + (1 * 6) = $31.