Find and correct the error.

Question

x/4+6>3

x+6>12

x>6

(1 point)
Responses

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

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

Answer 1

Let's solve the original inequality step by step and identify the error:

The original inequality is: \[ \frac{x}{4} + 6 > 3 \]

1. First, subtract 6 from both sides: \[ \frac{x}{4} > 3 - 6 \] \[ \frac{x}{4} > -3 \]

2. Now, multiply both sides by 4 to solve for \(x\): \[ x > -3 \times 4 \] \[ x > -12 \]

The error in the initial reasoning lies in the incorrect simplification of the inequality. The correct final inequality should indeed be: \[ x > -12 \]

So the correct response from the options given is: 6 should have been subtracted first before multiplying by 4 - the true answer should be x > -12.