2. Example 1: Writing Equivalent Equations
Main Idea
Example 1: Writing Equivalent Equations
Example 2: Equations with Variables on Each Side
Example 3: Real-World Example
Lesson Menu

3. Use the properties of equality to simplify and solve equations with variables on each side.
Main Idea/Vocabulary

4. Writing Equivalent Equations
Express 5x – 9 = x + 11 as an equivalent equation. Justify your answer.
Method 1 Subtract a Variable
5x – 9 = x + 11 Write the equation.
– x = – x Subtract x from each side.
4x – 9 = 11 Simplify.
Example 1

5. Writing Equivalent Equations
Method 2 Subtract a Number
5x – 9 = x + 11 Write the equation.
+ 9 = + 9 Add 9 to each side.
5x = x + 20 Simplify.
Answer: So, 5x – 9 = x + 11 is equivalent to 4x – 9 = 11 and 5x = x + 20.
Example 1

6. C. 9y + 2 = 20; subtract y from each side.
Express 10y + 2 = y + 20 as an equivalent equation. Justify your answer.
A. 11y + 2 = 20; add y to each side.
B. 10y = y + 22; add 2 to each side.
C. 9y + 2 = 20; subtract y from each side.
D. 10y + 22 = y; add 20 to each side.
Example 1 CYP

7. Equations with Variables on Each Side
Solve 8x = x − 49.
8x = x – 49 Write the equation.
8x – x = x – x – 49 Subtraction Property of Equality
7x = – 49 Simplify.
Division Property of Equality
x = – 7 Simplify.
Answer: The solution is x = –7.
Example 2

8. Equations with Variables on Each Side
Check
8x = x – 49 Write the original equation. ?
8(– 7) = – 7 – 49 Replace x with –7.
–56 = –56 The sentence is true. 
Example 2

9. Solve 11x = x − 60.
A. –6
B. 6
C. 5
D. 71
Example 2 CYP

10. 10x + 60 = 22x Write the equation.
GOLF At a community golf course, if you pay a one-time membership fee of $60, each round of golf you play costs $10. The price of a round of golf for nonmembers is $22. Write and solve an equation to find how many discounted rounds of golf you would need to buy to equal the cost of undiscounted rounds of golf. Let x represent the number of rounds purchased.
10x + 60 = 22x Write the equation.
10x – 10x + 60 = 22x – 10x Subtraction Property of Equality
60 = 12x Simplify.
Example 3

11. Division Property of Equality
5 = x Simplify.
Answer: You would need to buy 5 rounds.
Check
10x + 60 = 22x Write the original equation. ?
10(5) + 60 = 22(5) Replace x with 5.
110 = 110 The sentence is true. 
Example 3

12. COFFEE A coffee shop sells reusable coffee mugs for $6
COFFEE A coffee shop sells reusable coffee mugs for $6. The cost of a refill for the mug is $1.25. The cost of a cup of coffee without the mug is $1.50. Write and solve an equation to find how many coffee refills you would need to purchase to equal the cost of undiscounted cups of coffee. Let x represent the number of cups of coffee purchased.
A x = 1.50x; x = 24
B x = 1.25x; x = 12
C x = 1.50x; x = 6
D x = 1.50x; x = 1.5
Example 3 CYP