Solve each inequality. Give the solution set in interval notation. | 0.01x + 1 | < 0.01

Verified step by step guidance

1. Step 1: Recognize that the inequality \(|0.01x + 1| < 0.01\) is an absolute value inequality of the form \(|A| < B\), which can be rewritten as two separate inequalities: \(-B < A < B\).
2. Step 2: Apply the rule for absolute value inequalities to rewrite the given inequality as two separate inequalities: \(-0.01 < 0.01x + 1 < 0.01\).
3. Step 3: Solve the left inequality \(-0.01 < 0.01x + 1\) by subtracting 1 from both sides to isolate the term with \(x\): \(-1.01 < 0.01x\).
4. Step 4: Solve the right inequality \(0.01x + 1 < 0.01\) by subtracting 1 from both sides to isolate the term with \(x\): \(0.01x < -0.99\).
5. Step 5: Divide both sides of each inequality by 0.01 to solve for \(x\), and then express the solution set in interval notation.

Key Concepts

Absolute Value Inequalities

Absolute value inequalities express the distance of a variable from a certain point on the number line. The inequality |A| < B means that A is within B units of 0, leading to two simultaneous inequalities: -B < A < B. Understanding this concept is crucial for solving the given inequality.

Interval Notation

Interval notation is a mathematical notation used to represent a range of values. It uses brackets [ ] for inclusive endpoints and parentheses ( ) for exclusive endpoints. For example, the interval (a, b) includes all numbers greater than a and less than b, but not a and b themselves. This notation is essential for expressing the solution set of inequalities.

Solving Linear Inequalities

Solving linear inequalities involves isolating the variable on one side of the inequality sign. This process is similar to solving linear equations but requires careful attention to the direction of the inequality, especially when multiplying or dividing by negative numbers. Mastery of this concept is necessary to find the correct solution set for the given inequality.