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Johan found that the equation -218-x-6 = -12 had two possible solutions: x = 5 and x =-11. Which explains whether his solutions are correct? O He is correct because both solutions satisfy the equation. O He is not correct because he made aign error. O He is not correct because there are no solutions. He is not correct because there is only one solution: x = 5.

Johan found that the equation -218-x-6 = -12 had two possible solutions: x = 5 and x =-11. Which explains whether his solutions are correct? O He is correct because both solutions satisfy the equation. O He is not correct because he made aign error. O He is not correct because there are no solutions. He is not correct because there is only one solution: x = 5.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Problem Statement: Johan found that the equation \(-2|8 - x| - 6 = -12\) had two possible solutions: \(x = 5\) and \(x = -11\). Which explains whether his solutions are correct? ### Options: - \(\circ\) He is correct because both solutions satisfy the equation. - \(\circ\) He is not correct because he made a sign error. - \(\circ\) He is not correct because there are no solutions. - \(\circ\) He is not correct because there is only one solution: \(x = 5\). --- ### Analysis: To determine if Johan's solutions are correct, we need to verify if both \(x = 5\) and \(x = -11\) satisfy the equation \(-2|8 - x| - 6 = -12\). Let's solve this step-by-step. 1. **Substituting \(x = 5\):** - \(8 - x = 8 - 5 = 3\) - \(|8 - x| = |3| = 3\) - \(-2 \cdot 3 - 6 = -6 - 6 = -12\) - \(x = 5\) satisfies the equation. 2. **Substituting \(x = -11\):** - \(8 - x = 8 - (-11) = 8 + 11 = 19\) - \(|8 - x| = |19| = 19\) - \(-2 \cdot 19 - 6 = -38 - 6 = -44\) - \(x = -11\) does not satisfy the equation. Hence, only \(x = 5\) satisfies the given equation. Therefore, the correct explanation is: \(\circ\) He is not correct because there is only one solution: \(x = 5\).
Transcribed Image Text:### Problem Statement: Johan found that the equation \(-2|8 - x| - 6 = -12\) had two possible solutions: \(x = 5\) and \(x = -11\). Which explains whether his solutions are correct? ### Options: - \(\circ\) He is correct because both solutions satisfy the equation. - \(\circ\) He is not correct because he made a sign error. - \(\circ\) He is not correct because there are no solutions. - \(\circ\) He is not correct because there is only one solution: \(x = 5\). --- ### Analysis: To determine if Johan's solutions are correct, we need to verify if both \(x = 5\) and \(x = -11\) satisfy the equation \(-2|8 - x| - 6 = -12\). Let's solve this step-by-step. 1. **Substituting \(x = 5\):** - \(8 - x = 8 - 5 = 3\) - \(|8 - x| = |3| = 3\) - \(-2 \cdot 3 - 6 = -6 - 6 = -12\) - \(x = 5\) satisfies the equation. 2. **Substituting \(x = -11\):** - \(8 - x = 8 - (-11) = 8 + 11 = 19\) - \(|8 - x| = |19| = 19\) - \(-2 \cdot 19 - 6 = -38 - 6 = -44\) - \(x = -11\) does not satisfy the equation. Hence, only \(x = 5\) satisfies the given equation. Therefore, the correct explanation is: \(\circ\) He is not correct because there is only one solution: \(x = 5\).
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