Question

Solve the absolute value equations. $$|4 x+1|=6$$

Name: Problem 22, Chapter 1: Intermediate Algebra
Uploaded: 2020-06-15T09:51:52-08:00
Duration: 1 min 45 s
Channel: Ankit Gupta
Description: Solve the absolute value equations. |4 x+1|=6

   
Solve the absolute value equations.
$$|4 x+1|=6$$

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 1, Problem 22

Instant Answer

Solved by Expert Ankit Gupta

06/15/2020

Step 1

The absolute value of a number is always positive or zero. Therefore, the equation $|4x+1|=6$ can be rewritten as two separate equations: $4x+1=6$ and $4x+1=-6$. Show more…

Show all steps

Thanks for your feedback!

Solve the absolute value equations. $$|4 x+1|=6$$

Play audio

Feedback

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 refers to the distance of a number from zero on the number line, irrespective of its sign. In equations, it represents a non-negative quantity, making it essential to consider both positive and negative scenarios when solving.

Case Analysis in Absolute Value Equations

Solving absolute value equations typically involves breaking the equation into two separate cases: one where the expression inside the absolute value is non-negative and equals the given value, and one where it is negative and equals the negation of the given value. This systematic approach ensures that all potential solutions are considered.

Linear Equations

After splitting an absolute value equation into cases, each case typically results in a linear equation. Solving these linear equations involves applying standard algebraic techniques, like isolating the variable, to find the solution for each case.

Please give Ace some feedback