For what values of x will √((x-1)^2)=x-1 ? Explain how you...

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Key Concepts

Square Root Function as an Absolute Value

The square root of a squared expression, ?(a²), is defined as the absolute value of a. This is a fundamental property in algebra, indicating that the square root function yields the nonnegative value of any squared expression. Understanding this property is essential when simplifying expressions involving square roots and squared terms.

Definition and Properties of Absolute Value

The absolute value of a number is its distance from zero on the number line without regard to direction, meaning it is always nonnegative. This definition is used to rewrite equations involving square roots of squared expressions, and is key in determining when an equality holds true, especially when comparing expressions that might otherwise take negative values.

Solving Equations Involving Absolute Values

When solving equations that involve absolute values, it is important to consider the conditions under which the equation holds true, since the output of an absolute value function is always nonnegative. This often means determining separately where the expression inside the absolute value is nonnegative or negative, and then analyzing the resulting equations in each case to find the solution set.

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