An equation is shown below:

Question

12x + 3(x − 5) = 6x + 9x − 15

Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)

Part B: Name one property you used to solve this equation. (4 points)
In 2 sentences

Answer 1

Part A:
12x + 3(x − 5) = 6x + 9x − 15
12x + 3x - 15 = 6x + 9x - 15
15x - 15 = 15x - 15
0 = 0

This equation is an identity, so it has infinitely many solutions.

Part B:
To solve this equation, I used the distributive property to simplify the equation by distributing the 3 to both terms inside the parentheses.