Solve each equation or inequality. |18- 3x | 4 < -13

Key Concepts

Absolute Value

Absolute value measures the distance of a number from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|. For example, |3| = 3 and |-3| = 3. In equations or inequalities, the absolute value can create two scenarios: one where the expression inside is positive and another where it is negative.

Inequalities

Inequalities express a relationship between two values that are not necessarily equal, using symbols like <, >, ≤, or ≥. They indicate that one side is less than or greater than the other. Solving inequalities often involves similar steps to solving equations, but special care must be taken when multiplying or dividing by negative numbers, as it reverses the inequality sign.

Solving Equations

Solving equations involves finding the value(s) of the variable that make the equation true. This process often includes isolating the variable on one side of the equation through various algebraic operations. In the case of absolute value equations, it may require setting up two separate equations based on the definition of absolute value, allowing for a comprehensive solution.