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Find and correct the error.

x^4+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

1 answer

To correct the inequality provided:

The original inequality is:

  1. \( x^4 + 6 > 3 \)

We need to isolate \( x \):

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

This inequality is true for all real numbers \( x \) since any real number raised to the fourth power will be greater than or equal to 0.

Now, the next inequality given is:

  1. \( x + 6 > 12 \)

Subtract 6 from both sides: \[ x > 12 - 6 \] \[ x > 6 \]

This step is valid and correctly manipulated.

Considering the provided responses, it seems like the most relevant mistake is that in this chain of inequalities, no flipping of symbols was necessary as they weren't inequalities in the standard sense that would follow different rules under multiplication/division or addition/subtraction.

Thus, the correct understanding here is that:

  • The original setup gives a true statement for all \( x \) in \( x^4 > -3 \).
  • For \( x + 6 > 12 \), this simplifies correctly to \( x > 6 \).

None of the response options are correct as they misinterpret the inequalities. The inequality \( x > 6 \) stands correct as stated without needing further adjustments concerning the symbols or operation order.

Correct conclusion: \( x > 6 \) is accurate.