Solve. |3 x-2|=|2 x-3|

Name: Problem 452, Chapter 2: Intermediate Algebra
Uploaded: 2022-09-25T18:27:39-08:00
Channel: Suzanne W.
Description: Solve. |3 x-2|=|2 x-3|

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Key Concepts

Solving Linear Equations

Once the absolute value equation is divided into cases, each case often results in a simple linear equation. Solving these equations involves standard algebraic techniques such as isolating the variable, combining like terms, and performing arithmetic operations to identify the potential solutions.

Case Analysis in Absolute Value Equations

Equations that involve absolute values typically require splitting the problem into different cases based on the sign of the expression inside the absolute value. This approach allows one to remove the absolute value by considering separate linear scenarios where the expression is either nonnegative or negative.

Absolute Value

Absolute value is a mathematical operation that measures the distance of a number from zero on the number line, regardless of its direction. In equations, the absolute value function outputs the non-negative magnitude of an expression, simplifying the handling of negative numbers in computations.

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