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Chapter 1: Problem 85

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

Short Answer

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

Step by step solution

01

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 \(4x - 6 = 6x - 4\).
02

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 \(x = 1\).
03

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 \(1^{2} - 1 = 0\).

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