Solve each equation or inequality. |4x-12| ≥ -3

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 'a', the absolute value is defined as |a| = a if a ≥ 0, and |a| = -a if a < 0. This concept is crucial for understanding how to manipulate equations involving absolute values, as it leads to two possible cases based on the sign of the expression inside the absolute value.

Inequalities

Inequalities express a relationship between two expressions that are not necessarily equal. They can be strict (using < or >) or non-strict (using ≤ or ≥). In the context of solving inequalities, it is important to understand how to interpret and manipulate them, especially when involving absolute values, as they can lead to multiple solution sets.

Solution Sets

A solution set is the collection of all values that satisfy a given equation or inequality. When solving inequalities, particularly those involving absolute values, it is essential to determine the conditions under which the inequality holds true. In this case, since the absolute value is always non-negative, the inequality |4x - 12| ≥ -3 is always true, leading to the conclusion that the solution set includes all real numbers.