1. Equations with the Variable on Both Sides
11.1
How can you represent and solve equations with the variable on both sides?

2. ADDITIONAL EXAMPLE 1
Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. For how many hours is the total fee charged by the companies the same?
3 hours

3. 11.1 LESSON QUIZ 8.8.A, 8.8.B, 8.8.C Solve each equation. 1.
3x + 5 = –x – 7
x = –3 2.
3 – 5x = –9 + x
x = 2 3.
Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same.
2 hours

4. The numbers 5, 7, and 9 are an example of three consecutive odd integers. Write and solve an equation for the problem below.
Find three consecutive odd integers whose sum is 121 minus twice the first integer.
Let x = the first number, x + 2 = the second number, and x + 4 = the third number. Then x + (x + 2) + (x + 4) = 121 – 2x, or 5x = 115. Therefore, x = 23. The consecutive odd integers are 23, 25, and 27.

5. How can you represent and solve equations with the variable on both sides?
Sample answer:
You can use algebra tiles to model and solve equations with the variable on both sides. You can also use inverse operations to get the variable terms on one side of the equal sign and the constant terms on the other side, and then divide both sides by the coefficient of the resulting variable term.