Question

Solve and graph the solution set on a number line: $$ 3|2 x-1| \geq 21 $$

   Solve and graph the solution set on a number line:
$$
3|2 x-1| \geq 21
$$

College Algebra

College Algebra

Robert Blitzer 7th Edition

Chapter 2, Problem 102

Instant Answer

Solved by Expert Leslie Deeb

10/10/2022

Step 1

Step 1: First, we divide both sides of the inequality by 3 to isolate the absolute value expression: $$ |2x-1| \geq 7 $$ Show more…

Show all steps

lock

Thanks for your feedback!

Solve and graph the solution set on a number line: $$ 3|2 x-1| \geq 21 $$

Play audio

Feedback

Powered by NumerAI

Leslie Deeb and 94 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Absolute Value

Absolute value represents the distance of a number from zero on a number line, disregarding its sign. This concept is fundamental when dealing with expressions that measure distance or magnitude regardless of direction.

Solving Absolute Value Inequalities

This involves isolating the absolute value expression and then considering the two cases defined by the absolute value (one for the non-negative scenario and one for the negative). The methodology typically splits the inequality into a compound inequality that covers both possible scenarios.

Graphing on a Number Line

Graphing solution sets on a number line provides a visual representation of the values that satisfy an inequality. It involves marking boundary points and shading the regions corresponding to the solutions, with careful attention to whether endpoints are included or excluded.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later