Question

Find and correct the error.


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

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 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

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

Answer 1

To solve the inequality \( x^4 + 6 > 3 \), we first need to simplify it step by step.

1. Subtract 6 from both sides:

\[
x^4 > 3 - 6
\]

This simplifies to:

\[
x^4 > -3
\]

2. Since \( x^4 \) (the fourth power of any real number) is always non-negative (greater than or equal to 0), the inequality \( x^4 > -3 \) is true for all real values of \( x \).

Therefore, the error in the original reasoning lies in misunderstanding or manipulating the inequality incorrectly.

Now, looking at the provided response options, none of them accurately reflect the situation, as the inequality \( x^4 > -3 \) doesn't provide a specific constraint on \( x \) other than that it can be any real number.

So, the correct conclusion should be that the inequality \( x^4 + 6 > 3 \) holds true for all real \( x \).