Problem 85 - College Algebra Essentials

Question

Evaluate \(x^{2}-x\) for the value of \(x\) satisfying \(4(x-2)+2=4 x-2(2-x)\).

Step-by-Step Solution

Answer

The evaluated value of the function for the given value of \(x\) is 0.

Step 1: Simplify the Equation

Start by simplifying both sides of the equation. Distribute the 4 and -2 on the left and right side of the equation respectively. \(4x - 8 + 2 = 4x - 2(2 - x)\) simplifies to \(4x - 6 = 4x - 4 + 2x\). Combine like terms to result in \(4x - 6 = 6x - 4\).

Step 2: Solve for x

To isolate \(x\) on one side of the equation, subtract \(4x\) from both sides to get \(-2 = 2x - 4\). Add 4 to both sides to find \(x = 1\).

Step 3: Substitute x into the Original Function

Substitute the determined value \(x = 1\) into the original function \(x^{2}-x\). By doing so, the function becomes \(1^{2} - 1 = 0\).