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
3:22 minutes
Problem 44a
Textbook Question
Textbook QuestionSolve each equation or inequality. |8 - 3x| - 3 = -2
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|, and is always non-negative. For example, |5| = 5 and |-5| = 5. Understanding absolute value is crucial for solving equations that involve it, as it leads to two possible cases based on the definition.
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Linear Equations
A linear equation is an equation of the first degree, meaning it involves variables raised only to the power of one. The general form is ax + b = c, where a, b, and c are constants. Solving linear equations often involves isolating the variable on one side of the equation. In the context of absolute value, solving the equation may lead to two separate linear equations to consider.
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Inequalities
Inequalities express a relationship where one side is not necessarily equal to the other, using symbols like <, >, ≤, or ≥. When solving inequalities, the solution set can include a range of values rather than a single number. Understanding how to manipulate inequalities is essential, especially when absolute values are involved, as they can lead to multiple cases that need to be analyzed separately.
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