Solve each equation or inequality. | 4x+ 3| > 0

Key Concepts

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|. For example, |4| = 4 and |-4| = 4. Understanding absolute value is crucial for solving equations and inequalities that involve it, as it can lead 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 use symbols such as '>', '<', '≥', and '≤' to indicate whether one side is greater than, less than, or equal to the other. In the context of the given problem, solving the inequality |4x + 3| > 0 requires determining the values of x for which the expression is not equal to zero, leading to a range of solutions.

Solution Sets

A solution set is the collection of all values that satisfy a given equation or inequality. For the inequality |4x + 3| > 0, the solution set includes all real numbers except those that make the expression inside the absolute value equal to zero. Understanding how to express and interpret solution sets is essential for effectively communicating the results of solving algebraic problems.