Solve each inequality. Give the solution set in interval notation. | 5/3 - (1/2) x | > 2/9

Verified step by step guidance

1. Start by isolating the absolute value expression: \(|\frac{5}{3} - \frac{1}{2}x| > \frac{2}{9}\).
2. Recognize that the inequality \(|A| > B\) implies two separate inequalities: \(A > B\) or \(A < -B\).
3. Set up the first inequality: \(\frac{5}{3} - \frac{1}{2}x > \frac{2}{9}\).
4. Set up the second inequality: \(\frac{5}{3} - \frac{1}{2}x < -\frac{2}{9}\).
5. Solve each inequality separately for \(x\) and express the solution set in interval notation.

Key Concepts

Absolute Value Inequalities

Absolute value inequalities involve expressions that measure the distance of a number from zero on the number line. The inequality |A| > B indicates that A is either greater than B or less than -B. Understanding how to split the absolute value into two separate inequalities is crucial for solving these types of problems.

Interval Notation

Interval notation is a mathematical notation used to represent a range of values. It uses parentheses and brackets to indicate whether endpoints are included (closed interval) or excluded (open interval). For example, (a, b) means all numbers between a and b, not including a and b, while [a, b] includes both endpoints.

Solving Linear Inequalities

Solving linear inequalities involves finding the values of a variable that satisfy the inequality. This process often includes isolating the variable on one side of the inequality sign and may require reversing the inequality when multiplying or dividing by a negative number. The solution set can then be expressed in interval notation.