1. The learner will solve equations with variables on both sides
Objective
The learner will solve equations with variables on both sides

2. Equations with Variables on Both Sides Pages 96 - 101
Lesson 2 - 4
Equations with Variables on Both Sides
Pages

3. Video
Solving Equations with Variables on Both Sides of Equations

4. To solve an equation that has variables on both sides, use the Addition or Subtraction Properties of Equality to get the variables on one side of the equation.
Find the value of x.
6x + 3 = 8x – 21

5. a. -6d = d + 4 b. 2(c – 6) = 9c + 2 c. m – 5 = 3m d. 7k – 4 = 5k + 16
Solve each equation:
a. -6d = d + 4
b. 2(c – 6) = 9c + 2
c. m – 5 = 3m
d. 7k – 4 = 5k + 16

6. You can buy used in-line skates from your friend for $40, or you can rent some. Either way, you must rent safety equipment. How many hours must you skate for the cost of renting and buying skates to be the same? Safety equipment is $1.50 per hour and safety equipment and skate rental together is $3.50 per hour.

7. Define: Let h = number of hours you must skate
Write: h = 3.5h
h – 1.5h = 3.5h – 1.5h (subtract)
40 = 2h
(combine like terms)
40/2 = 2h/2 (divide)
20 = h
You would have to skate 20 hours for the cost to be the same.

8. A hairdresser is considering ordering a certain shampoo
A hairdresser is considering ordering a certain shampoo. Company A charges $4 per 8oz bottle plus a $10 handling fee per order. Company B charges $3 per 8oz bottle plus a $25 handling fee per order. How many bottles must the hairdresser buy to justify using Company B?

9. An equation has no solution if no value of the variable makes the equation true.
The equation 2x = 2x + 1 has no solution.
An equation that is true for every value of the variable is an identity.
The equation 2x = 2x is an identity.

10. 10 – 8a = 10 – 8a 10 – 8a + 8a = 10 – 8a + 8a 10 = 10 (identity)
Solve: 10 – 8a = 2(5 – 4a)
10 – 8a = 10 – 8a
10 – 8a + 8a = 10 – 8a + 8a
10 = 10 (identity)
a = all real numbers

11. Solve 6m – 5 = 7m + 7 – m
6m – 5 = 6m + 7
6m – 5 – 6m = 6m + 7 – 6m
-5 = 7 (never true)
So this equation has no solution.

12. Determine whether each equation is an identity or whether it has no solution.
9 + 5n = 5n – 1
9 + 5x = 7x + 9 – 2x

13. Open Workbooks
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