Find and correct the error.

Question

x4+6>3

x+6>12

x>6

(1 point)
Responses

6 should have been subtracted first before multiplying by 4 - the true answer should be x > -3/4
6 should have been subtracted first before multiplying by 4 - the true answer should be x > -3/4

6 should have been subtracted first before multiplying by 4 - the true answer should be x > -12
6 should have been subtracted first before multiplying by 4 - the true answer should be x > -12

With inequalities you always flip the symbol at the end - the true answer should be x < 6
With inequalities you always flip the symbol at the end - the true answer should be x < 6

6 should have been added first before multiplying by 4 - the true answer should be x > 36
6 should have been added first before multiplying by 4 - the true answer should be x > 36
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Answer 1

To find and correct the error in the inequality \( x^4 + 6 > 3 \), we will solve it step by step.

1. Start with the original inequality: \[ x^4 + 6 > 3 \]

2. Subtract 6 from both sides: \[ x^4 > 3 - 6 \] \[ x^4 > -3 \]

Now, any real number raised to the fourth power will always be greater than or equal to 0. Thus, \( x^4 > -3 \) is true for all real values of \( x \).

Next, let's analyze the other statement given:

\[ x + 6 > 12 \]

Subtracting 6 from both sides, we get: \[ x > 6 \]

None of the responses correctly address the issue with \( x^4 + 6 > 3 \). The answer should be that \( x^4 > -3 \), which is always true for real numbers.

The second inequality \( x + 6 > 12 \) leads to \( x > 6 \), which is correct.

Therefore, the correct path is to note that these inequalities do not require further specific adjustments based on the options given. The first inequality status means \( x \) can be any real number, while the second means \( x \) specifically must be greater than 6.

Conclusion:

The responses do not correctly identify the proper simplification of the inequalities or their resolutions. Thus, an appropriate summary of the findings is:

1. The first inequality \( x^4 + 6 > 3 \) simplifies to \( x^4 > -3 \), which is true for all \( x \in \mathbb{R} \).
2. The second inequality \( x + 6 > 12 \) correctly simplifies to \( x > 6 \).

There is no error among the listed responses that accurately reflects the inequalities' resolutions.