step 1 We have to solve for x. We have been given that absolute value of x plus absolute value of 3x mi

Solve |x+| 3 x-||2=2

Name: Problem 94, Chapter 1: College Algebra
Uploaded: 2020-04-21T16:41:53-08:00
Duration: 1 min 32 s
Channel: Ankit Gupta
Description: Solve |x+| 3 x-||2=2

Key Concepts

Nested Absolute Value Equations

Nested absolute value equations involve an absolute value expression contained inside another absolute value. Solving these equations requires careful step-by-step analysis, first resolving the inner absolute value by its piecewise definition and then applying the outer absolute value properties to arrive at the complete solution.

Case Analysis Method

The case analysis method is central to solving equations with absolute values. It involves dividing the domain into distinct cases based on the sign of the expression inside the absolute value, allowing each scenario to be analyzed with simpler linear equations. This systematic approach ensures all possibilities are considered in finding the solution.

Absolute Value Function

The absolute value function measures the non-negative distance of a number from zero. It fundamentally transforms any negative input into its positive counterpart while leaving non-negative inputs unchanged, serving as the basis for handling distance and magnitude in various algebraic problems.

Piecewise Analysis

Absolute value expressions can be interpreted as piecewise-defined functions, where the expression inside may take on different behaviors depending on whether it is positive or negative. This piecewise breakdown simplifies equations into multiple conditions or cases that must each be solved separately.

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