Solving the Equation: 6(3x+1) - 3(4x-2) = 2(x-5) = 3(2x-2)
In this article, we will solve the given equation step by step.
Given Equation: 6(3x+1) - 3(4x-2) = 2(x-5) = 3(2x-2)
Step 1: Expand the Brackets Let's start by expanding the brackets on both sides of the equation:
6(3x+1) = 18x + 6 -3(4x-2) = -12x + 6 2(x-5) = 2x - 10 3(2x-2) = 6x - 6
Now, the equation becomes:
18x + 6 - 12x + 6 = 2x - 10 = 6x - 6
Step 2: Simplify the Equation Combine like terms on the left side of the equation:
6x + 12 = 2x - 10 = 6x - 6
Step 3: Equate the Expressions Since the equation is an equality, we can equate the expressions:
6x + 12 = 2x - 10 6x + 12 = 6x - 6
Step 4: Solve for x Now, let's solve for x:
6x - 2x = -10 - 12 4x = -22 x = -22/4 x = -11/2
Final Answer: The value of x is -11/2.
Therefore, the solution to the equation 6(3x+1) - 3(4x-2) = 2(x-5) = 3(2x-2) is x = -11/2.
