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 Equations

College Algebra

1. Equations & Inequalities

Linear Equations

0:59 minutes

Problem 107

Textbook Question

Solve each equation or inequality. |x+4| = 7

Verified Solution

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

Video duration:

59s

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

Absolute value measures the distance of a number from zero on the number line, regardless of direction. For any real number x, the absolute value is denoted as |x| and is defined as |x| = x if x ≥ 0, and |x| = -x if x < 0. Understanding absolute value is crucial for solving equations that involve it, as it leads to two possible cases based on the definition.

Solving Equations

Solving equations involves finding the values of variables that make the equation true. In the case of absolute value equations, such as |x + 4| = 7, we set up two separate equations: x + 4 = 7 and x + 4 = -7. This process requires isolating the variable and simplifying to find the solutions.

Inequalities

Inequalities express a relationship where one side is not necessarily equal to the other, using symbols like <, >, ≤, or ≥. While the given question focuses on an equation, understanding inequalities is important as they often arise in similar contexts, especially when dealing with absolute values, which can lead to ranges of solutions rather than discrete values.