Solve the absolute value inequalities. Graph the solution set and write the solution in interval

step 1 We want to solve and graph the absolute value inequality, negative 3 times the absolute value of

Solve the absolute value inequalities. Graph the solution...

Key Concepts

Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is a fundamental concept in algebra that simplifies the handling of distance and magnitude, and it is defined as the non-negative value of a real number.

Solving Absolute Value Inequalities

Solving absolute value inequalities involves determining the set of values that satisfy the condition involving the absolute value, often by rewriting the inequality as a compound inequality. This process typically includes isolating the absolute value expression and then considering the two cases that arise from its definition.

Properties of Inequalities

When working with inequalities, especially those involving negative coefficients, it is important to understand that multiplying or dividing both sides of an inequality by a negative number reverses the direction of the inequality. This property is crucial in correctly solving and transforming the inequality.

Interval Notation

Interval notation is a concise way to represent a set or range of numbers. It uses parentheses and brackets to denote whether endpoints are included or excluded from the set, making it an essential tool for expressing solution sets in algebra.

Graphing on a Number Line

Graphing on a number line provides a visual representation of a solution set. By marking the interval corresponding to the solution, one can easily illustrate which values are included, offering a clear depiction of the range of numbers that satisfy the inequality.

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