Question

For what values of $x$ will $\sqrt{(2 x-6)^{2}}=2 x-6$ ? Explain how you determined your answer.

Name: Problem 115, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2020-06-29T20:10:56-08:00
Duration: 1 min
Channel: Jeffrey Morris
Description: For what values of x will √((2 x-6)^2)=2 x-6 ? Explain how you determined your answer.

    For what values of $x$ will $\sqrt{(2 x-6)^{2}}=2 x-6$ ? Explain how you determined your answer.

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 115

Instant Answer

Solved by Expert Jeffrey Morris

06/29/2020

Step 1

Now, we know that the square root of a number squared is the absolute value of that number. So, we can rewrite the equation as $|2x-6| = 2x-6$. We have two cases to consider: 1) When $2x-6$ is positive or zero, the equation becomes $2x-6 = 2x-6$. This is Show more…

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Key Concepts

Square Root and Absolute Value Relationship

Taking the square root of a square yields the absolute value of the original expression. This means that for any real expression u, ?(u²) equals |u|, not simply u. Recognizing this relationship is vital when dealing with equations that contain the square root of a squared term.

Conditions for Absolute Value Equality

An equation of the form |u| = u holds true if and only if u is nonnegative (u ? 0). This condition ensures that the absolute value does not alter the original expression, which is key when solving equations and applying restrictions to the variable.

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