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

0:53 minutes

Problem 60a

Textbook Question

Solve each equation or inequality. | 7 + 2x| = 0

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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 measures the distance of a number from zero on the number line, regardless of direction. For any real number 'a', the absolute value is defined as |a| = a if a ≥ 0, and |a| = -a if a < 0. In the context of equations, setting an absolute value expression equal to zero indicates that the expression inside must also equal zero.

Solving Equations

Solving equations involves finding the values of variables that make the equation true. In this case, we need to isolate the variable 'x' by manipulating the equation. Understanding how to perform operations such as addition, subtraction, multiplication, and division is essential for solving equations effectively.

Zero Property of Absolute Value

The zero property of absolute value states that the only time an absolute value expression equals zero is when the expression inside the absolute value is also zero. This means that for |A| = 0, A must equal 0. This property is crucial for determining the solutions to equations involving absolute values.