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)
Please explain 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

Since 0 = 0 is always true, this equation has infinite solutions.

Part B:

One property used to solve this equation is the distributive property. This property allows us to distribute the number outside the parentheses to each term inside the parentheses.