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 Equations

College Algebra

1. Equations & Inequalities

Linear Equations

Previous problemNext problem

1:41 minutes

Problem 75

Textbook Question

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution.|2x - 1| + 3 = 3

Verified step by step guidance

Step 1: Isolate the absolute value expression.

Step 2: Subtract 3 from both sides of the equation to get |2x - 1| = 0.

Step 3: Set up two separate equations to solve for x: 2x - 1 = 0 and 2x - 1 = 0.

Step 4: Solve each equation for x.

Step 5: Check the solutions in the original equation to ensure they are valid.

Verified video answer for a similar problem:

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

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, |3| = 3 and |-3| = 3. Understanding absolute value is crucial for solving equations that involve it, as it leads to two possible cases based on the definition.

Solving Absolute Value Equations

To solve an absolute value equation, you typically isolate the absolute value expression and then set up two separate equations: one for the positive case and one for the negative case. For instance, if |A| = B, then A = B or A = -B. This method allows you to find all possible solutions that satisfy the original equation.

Checking for Extraneous Solutions

After solving an equation, it is essential to check each solution in the original equation to ensure they are valid. This is particularly important in absolute value equations, as the process of squaring or isolating terms can introduce extraneous solutions that do not satisfy the original equation. Validating solutions helps confirm their correctness.