Solving an Algebraic Equation with a Contradiction
The image shows the following algebraic equation:
-4x + 8x - 3 = 8x - 1/2 (8x - 4)
Let's solve this step by step.
Firstly, combine like terms on the left side of the equation:
4x - 3 = 8x - 1/2 (8x - 4)
Now we need to distribute the 1/2 on the right side of the equation:
4x - 3 = 8x - (1/2 * 8x) + (1/2 * 4)
Simplify the products:
4x - 3 = 8x - 4x + 2
Combine like terms on the right side of the equation:
4x - 3 = 4x + 2
Now, we can subtract 4x from both sides to isolate the constant terms:
4x - 4x - 3 = 4x - 4x + 2
Which simplifies to:
-3 = 2
This results in a clear contradiction as -3 cannot equal 2. Therefore, there is no solution to the equation, indicating that it is inconsistent. This type of equation is also known as a contradiction because it indicates that there was probably a mistake in the formulation of the original problem or it's a system with no intersection points.
