Question

Solve the equation. $$20+|2 x-4|=15$$

   Solve the equation.
$$20+|2 x-4|=15$$

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 1, Problem 18

Instant Answer

Solved by Expert Ankit Gupta

07/28/2020

Step 1

Step 1: We start with the given equation: $$20+|2 x-4|=15$$ Subtract 20 from both sides to isolate the absolute value: $$|2 x-4|=15-20$$ This simplifies to: $$|2 x-4|=-5$$ Show more…

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Solve the equation. $$20+|2 x-4|=15$$

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Key Concepts

Absolute Value Function

The absolute value function measures the distance of a number from zero, always resulting in a nonnegative value. It is defined piecewise and is fundamental in understanding how expressions behave regardless of their sign.

Equations Involving Absolute Value

Equations that contain absolute value expressions require special attention because the absolute value impacts the sign of the inner expression. Solving these equations often involves considering different cases based on the possible values of the expression inside the absolute value.

Isolation of the Absolute Value Term

A common strategy in solving absolute value equations is to isolate the absolute value term on one side of the equation. This step is crucial because it allows the proper application of the definition of absolute value and assists in identifying any inherent restrictions on the solution.

Extraneous Solutions

When manipulating equations, particularly those involving absolute values, it is important to check whether the solutions obtained are valid for the original equation. This is because operations such as isolating the absolute value can sometimes lead to results that do not satisfy the initial conditions of the equation.

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