An equation is shown below:
4x + 2(x − 3) = 4x + 2x − 11
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:
4x + 2(x − 3) = 4x + 2x − 11
4x + 2x - 6 = 4x + 2x - 11 (distribute the 2)
6x - 6 = 6x - 11 (combine like terms)
6x - 6x = -11 + 6 (subtract 6x from both sides)
-6 = -5 (add 6 to both sides)
There are no solutions to this equation.
Part B:
One property used to solve this equation is the distributive property, which allows us to multiply a number by a group of numbers added together by multiplying each number inside the group by the number outside the parentheses.