An equation is shown below:
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)
Part A:
12x + 3(x − 5) = 6x + 9x − 15
12x + 3x - 15 = 6x + 9x - 15
15x - 15 = 15x - 15
Since the variables on both sides canceled out, we are left with -15 = -15. This means that the equation is true for all values of x.
Therefore, the equation has infinitely many solutions.
Part B:
One property used to solve this equation is the distributive property, where we distributed the 3 to both terms inside the parentheses: 3(x - 5) = 3x - 15.