Question - Solving an Algebraic Equation with a Contradiction
Solution:
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 + 2Combine like terms on the right side of the equation:4x - 3 = 4x + 2Now, we can subtract 4x from both sides to isolate the constant terms:4x - 4x - 3 = 4x - 4x + 2Which simplifies to:-3 = 2This 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.
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