Solve the absolute value equations. -2|x+3|=5

Name: Problem 35, Chapter 1: Intermediate Algebra
Uploaded: 2020-06-15T09:57:18-08:00
Duration: 32 s
Channel: Ankit Gupta
Description: Solve the absolute value equations. -2|x+3|=5

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Key Concepts

Solving Absolute Value Equations

When solving equations with absolute value expressions, the approach typically involves isolating the absolute value term and considering the implications of its non-negative nature. This might involve setting up different cases based on the definition of absolute value or examining the structure of the equation to see if it can be satisfied.

Interpreting Coefficients and Equation Feasibility

Multiplying an absolute value expression by a coefficient can change the behavior of the equation. Since absolute value expressions are non-negative, multiplying them by a negative coefficient results in a non-positive quantity. Recognizing this, one must check the feasibility of the equation when it is equated to a value that might contradict this inherent property, which can lead to the conclusion that no solution exists.

Absolute Value

The absolute value of a number is its distance from zero on the number line, which means it is always non-negative. This basic property is crucial when solving equations involving absolute value expressions, as it limits the range of possible outputs.

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