Solving the Equation: 1/2(x-1)-(x-3)=1/3(x+3)+1/6
In this article, we will solve the equation 1/2(x-1)-(x-3)=1/3(x+3)+1/6. To solve this equation, we need to follow the order of operations (PEMDAS) and simplify the equation step by step.
Step 1: Simplify the Left Side
The left side of the equation is 1/2(x-1)-(x-3). To simplify this expression, we can start by evaluating the parentheses.
1/2(x-1) = 1/2x - 1/2 -(x-3) = -x + 3
So, the left side of the equation becomes:
1/2x - 1/2 - x + 3
Step 2: Simplify the Right Side
The right side of the equation is 1/3(x+3)+1/6. To simplify this expression, we can start by evaluating the parentheses.
1/3(x+3) = 1/3x + 1 1/6 = 1/6
So, the right side of the equation becomes:
1/3x + 1 + 1/6
Step 3: Equate the Two Expressions
Now that we have simplified both sides of the equation, we can equate them:
1/2x - 1/2 - x + 3 = 1/3x + 1 + 1/6
Step 4: Solve for x
To solve for x, we can start by combining like terms on both sides of the equation:
-1/2x + 3 = 1/3x + 5/6
Next, we can add 1/2x to both sides of the equation to get:
3 = 5/6x + 5/6
Subtracting 5/6 from both sides gives us:
13/6 = 5/6x
Multiplying both sides by 6/5 gives us:
x = 13/5
Therefore, the solution to the equation is x = 13/5.