%2F(2)(x%2B6)%3D(1)%2F(2)x-9.jpeg "(1)/(2)(x+6)=(1)/(2)x-9")
Solving the Equation: (1/2)(x+6) = (1/2)x - 9
This article will guide you through the steps of solving the equation (1/2)(x+6) = (1/2)x - 9. We will use the principles of algebra to isolate the variable x and find its value.
1. Distribute the 1/2 on the left side:
The first step is to distribute the (1/2) on the left side of the equation. This gives us:
(1/2)x + 3 = (1/2)x - 9
2. Subtract (1/2)x from both sides:
To simplify the equation, we need to eliminate the x terms from one side. Subtracting (1/2)x from both sides results in:
(1/2)x + 3 - (1/2)x = (1/2)x - 9 - (1/2)x
This simplifies to:
3 = -9
3. Analyze the result:
The equation 3 = -9 is a contradiction. This means there is no solution to the original equation. The equation (1/2)(x+6) = (1/2)x - 9 has no solution because the x terms cancel out, leaving an impossible statement.
Conclusion: The equation (1/2)(x+6) = (1/2)x - 9 is an inconsistent equation with no solution. This can be determined by simplifying the equation through algebraic manipulation and observing the resulting contradiction.