1/3 (6x – 5) – X = 1/3 – 2(x + 1)

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Jun 16, 2024

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Solving the Equation: 1/3 (6x – 5) – x = 1/3 – 2(x + 1)

In this article, we will solve the equation 1/3 (6x – 5) – x = 1/3 – 2(x + 1). To do this, we will follow the order of operations (PEMDAS) and use basic algebraic properties to isolate the variable x.

Step 1: Simplify the Left Side of the Equation

First, let's simplify the left side of the equation:

1/3 (6x – 5) – x = ?

To simplify this expression, we will start by distributing the 1/3 to the terms inside the parentheses:

= 2x - 5/3 - x

Next, we will combine like terms:

= x - 5/3

So, the left side of the equation is x - 5/3.

Step 2: Simplify the Right Side of the Equation

Now, let's simplify the right side of the equation:

1/3 – 2(x + 1) = ?

To simplify this expression, we will start by distributing the 2 to the terms inside the parentheses:

= 1/3 - 2x - 2

Next, we will combine like terms:

= -2x - 1/3 - 2

Step 3: Equate the Two Expressions

Now that we have simplified both sides of the equation, we can equate them:

x - 5/3 = -2x - 1/3 - 2

Step 4: Solve for x

To solve for x, we will add 2x to both sides of the equation:

3x - 5/3 = -1/3 - 2

Next, we will add 5/3 to both sides of the equation:

3x = -1/3 + 5/3 - 2

= -1/3 + 5/3 - 2

= -2

Finally, we will divide both sides of the equation by 3:

x = -2/3

Therefore, the value of x is -2/3.