Table of contents

0. Review of Algebra4h 16m
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 19m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Inequalities

College Algebra

1. Equations & Inequalities

Linear Inequalities

1:15 minutes

Problem 53b

Textbook Question

Solve each equation or inequality. | 3x- 7 | + 1 < -2

Verified Solution

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

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

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, |3| = 3 and |-3| = 3. In equations and inequalities, absolute values can create two separate cases to consider, as they can be either positive or negative.

Inequalities

Inequalities express a relationship where one side is not equal to the other, using symbols like <, >, ≤, or ≥. They indicate that one quantity is less than or greater than another. Solving inequalities often involves similar steps to solving equations, but requires careful consideration of the direction of the inequality when multiplying or dividing by negative numbers.

Solving Compound Inequalities

Compound inequalities involve two or more inequalities that are connected by 'and' or 'or'. To solve them, one must find the values that satisfy all parts of the inequality. In the context of absolute value inequalities, this often leads to breaking the problem into two separate cases, allowing for a comprehensive solution that encompasses all possible scenarios.