Solve each equation or inequality. |x+10| = |x-11|

Key Concepts

Absolute Value

Absolute value measures the distance of a number from zero on the number line, regardless of direction. For any real number x, the absolute value is defined as |x| = x if x ≥ 0, and |x| = -x if x < 0. This concept is crucial for solving equations involving absolute values, as it leads to the creation of two separate cases to consider.

Equations with Absolute Values

When solving equations that involve absolute values, such as |A| = |B|, it is essential to recognize that this implies two scenarios: A = B and A = -B. This duality arises because both A and B can be equal in magnitude but differ in sign. Understanding this principle allows for the correct formulation of equations to find all possible solutions.

Solving Linear Equations

Linear equations are equations of the first degree, meaning they involve variables raised only to the power of one. To solve these equations, one typically isolates the variable on one side of the equation. Mastery of this technique is necessary for simplifying the cases derived from absolute value equations and finding the final solutions.