Solving the Equation (x/4) + 3(1 - 2x/4) = 0 to find the value of x

To solve the given equation (x/4) + 3(1 - 2x/4) = 0, we will follow the steps below:

Step 1: Simplify the equation
Let's simplify the given equation by applying the distributive property and simplifying the terms:

(x/4) + 3(1 - 2x/4) = 0

(x/4) + 3 - 6x/4 = 0

Step 2: Combine like terms
Combine the terms with x/4 and -6x/4:

(x/4 - 6x/4) + 3 = 0

(-5x/4) + 3 = 0

Step 3: Move the constant term to the other side
To isolate the variable x, we need to move the constant term 3 to the other side of the equation:

(-5x/4) = -3

Step 4: Solve for x
To solve for x, we will multiply both sides of the equation by the reciprocal of -5/4, which is -4/5:

(-5x/4) * (-4/5) = -3 * (-4/5)

x = 12/5

Step 5: Check the solution
To ensure that the obtained value of x is correct, we will substitute it back into the original equation and check if it satisfies the equation:

(x/4) + 3(1 - 2x/4) = 0

(12/5)/4 + 3(1 - 2(12/5)/4) = 0

3/5 + 3(1 - 6/5) = 0

3/5 + 3(5/5 - 6/5) = 0

3/5 + 3(-1/5) = 0

3/5 - 3/5 = 0

0 = 0

Since the equation is true when x = 12/5, we can conclude that the solution is correct.

Therefore, the value of x that satisfies the given equation is x = 12/5.