Question

Solve the absolute value equations. $$|x|+5=11$$

Name: Problem 9, Chapter 1: Intermediate Algebra
Uploaded: 2020-06-15T09:47:09-08:00
Duration: 46 s
Channel: Ankit Gupta
Description: Solve the absolute value equations. |x|+5=11

   Solve the absolute value equations.
$$|x|+5=11$$

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 1, Problem 9

Instant Answer

Solved by Expert Ankit Gupta

06/15/2020

Step 1

We can do this by subtracting 5 from both sides of the equation: $$|x|+5-5=11-5$$ Show more…

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Solve the absolute value equations. $$|x|+5=11$$

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Key Concepts

Absolute Value

Absolute value represents the distance of a number from zero on the number line, irrespective of its sign. It is always non-negative and forms the foundation for understanding equations where the magnitude of the variable, rather than its sign, is of interest.

Isolating the Absolute Value Expression

When solving equations that include an absolute value, the first step is to isolate the absolute value expression on one side of the equation. By doing so, you simplify the equation and prepare it for applying further methods pertinent to absolute value problems.

Splitting the Equation into Cases

Once the absolute value expression is isolated, the equation |expression| = value, where value is non-negative, leads to two separate cases: one where the expression equals the positive value and another where it equals the negative value. This process accounts for both potential scenarios that satisfy the absolute value definition.

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