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

Verified step by step guidance

1. Start by simplifying both sides of the equation: 4(x - 2) + 2 = 4x - 2(2 - x).
2. Distribute the terms: 4x - 8 + 2 = 4x - 4 + 2x.
3. Combine like terms: 4x - 6 = 6x - 4.
4. Rearrange the equation to isolate x: 4x - 6x = -4 + 6.
5. Solve for x: -2x = 2, then divide by -2 to find x.

Key Concepts

Solving Linear Equations

To solve the equation 4(x - 2) + 2 = 4x - 2(2 - x), one must isolate the variable x. This involves distributing terms, combining like terms, and rearranging the equation to find the value of x. Understanding how to manipulate equations is crucial for determining the correct value to substitute into the quadratic expression.

Quadratic Expressions

A quadratic expression is a polynomial of degree two, typically in the form ax^2 + bx + c. In this case, x^2 - x is a simple quadratic expression. Evaluating this expression requires substituting the value of x obtained from the previous step, which will yield a numerical result.

Substitution

Substitution is the process of replacing a variable in an expression with a specific value. After solving the linear equation for x, substituting this value into the quadratic expression x^2 - x allows for the evaluation of the expression. This concept is fundamental in algebra as it connects different parts of a problem.