1/2(x-1)-(x-3)=1/3(x+3)+1/6

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Jun 16, 2024

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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.