Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Inequalities

College Algebra

1. Equations & Inequalities

Linear Inequalities

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1:16 minutes

Problem 53

Textbook Question

In Exercises 51–58, solve each compound inequality.- 3 ≤ x - 2 < 1

Verified step by step guidance

Start by addressing the compound inequality: -3 \leq x - 2 < 1.

To isolate x, add 2 to each part of the compound inequality.

This results in: -3 + 2 \leq x < 1 + 2.

Simplify both sides to get: -1 \leq x < 3.

The solution is the set of x values that satisfy both inequalities, which can be expressed as an interval.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Compound Inequalities

A compound inequality consists of two or more inequalities that are combined into one statement by the words 'and' or 'or'. In this case, the compound inequality '3 ≤ x - 2 < 1' indicates that x must satisfy both conditions simultaneously. Understanding how to interpret and solve these inequalities is crucial for finding the values of x that meet the criteria.

Solving Inequalities

Solving inequalities involves isolating the variable on one side of the inequality sign. This process is similar to solving equations but requires special attention to the direction of the inequality sign, especially when multiplying or dividing by negative numbers. Mastery of this technique is essential for accurately determining the solution set for compound inequalities.

Interval Notation

Interval notation is a way of expressing the solution set of inequalities using intervals. It uses brackets and parentheses to indicate whether endpoints are included or excluded. For example, the solution to the compound inequality can be expressed in interval notation, which provides a clear and concise way to represent the range of values that satisfy the inequality.