Question

Find and correct the error.


x4+6>3

x+6>12

x>6

(1 point)
Responses

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

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

Answer 1

Let's analyze the original inequality step by step:

1. The inequality provided is \( x^4 + 6 > 3 \).
2. First, we need to isolate \( x^4 \):
\[
x^4 + 6 > 3
\]
Subtract 6 from both sides:
\[
x^4 > 3 - 6 \\
x^4 > -3
\]

Since \( x^4 \) is always non-negative (as any real number raised to an even power is greater than or equal to zero), this means that \( x^4 > -3 \) is true for all real numbers.

Therefore, the correct response does not seem to be found in the given options since there is no specific value for \( x \) that would restrict the solution set.

None of the provided answers accurately address the situation as stated. If you follow the original thought process of manipulating the inequality, it did not contain a step requiring multiplying or flipping an inequality sign.

So, the first step should have been to correctly state that the inequality \( x^4 > -3 \) holds for all real numbers \( x \).