Find and correct the error.

Question

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

Answer 1

Let's solve the inequality step by step to identify the error.

Original inequality: \[ \frac{x}{4} + 6 > 3 \]

Step 1: Subtract 6 from both sides: \[ \frac{x}{4} > 3 - 6 \] \[ \frac{x}{4} > -3 \]

Step 2: Multiply both sides by 4 (note that since we are multiplying by a positive number, we do not flip the inequality): \[ x > -12 \]

Now, looking at the responses given, the correct verification is that the final answer from our calculation is \( x > -12 \).

The correct option in the responses is: 6 should have been subtracted first before multiplying by 4 - the true answer should be x > -12.