Question

Select a value for $x$ for which $\sqrt{(2 x+1)^{2}} \neq 2 x+1$.

Name: Problem 93, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2020-06-23T17:19:22-08:00
Duration: 1 min 31 s
Channel: Ashley Jordon
Description: Select a value for x for which √((2 x+1)^2) ≠2 x+1.

   Select a value for $x$ for which $\sqrt{(2 x+1)^{2}} \neq 2 x+1$.

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 93

Instant Answer

Solved by Expert Ashley Jordon

06/23/2020

Step 1

For example, let's take x = -1. Now, substitute x = -1 into the expression: (2(-1) + 1)^2 = (-1)^2 = 1 The square root of 1 is 1. However, substituting x = -1 into the right side of the equation: Show more…

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Select a value for $x$ for which $\sqrt{(2 x+1)^{2}} \neq 2 x+1$.

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Key Concepts

Conditions for Equality and Inequality

When considering expressions like sqrt((2x+1)^2) which equal |2x+1|, equality to 2x+1 holds if 2x+1 is nonnegative. The expression |2x+1| is not equal to 2x+1 when 2x+1 is negative. Thus, to find values of x making the two expressions unequal, one needs to identify when 2x+1 < 0.

Square Root of a Square

The expression sqrt(s^2) simplifies to the absolute value of s, written as |s|. This is because squaring a number always yields a nonnegative result, and the square root, as a function, returns the nonnegative value whose square is the given input.

Absolute Value Function

The absolute value function, denoted by |s|, outputs the nonnegative magnitude of a number regardless of its sign. This property implies that if s is negative, then |s| equals -s, making it different from s itself whenever s is not already nonnegative.

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