Answer:
![x1](https://tex.z-dn.net/?f=x%3C-%5Cfrac%7B1%7D%7B2%7D%5Ctext%7B%20or%20%7D%20x%3E1)
Step-by-step explanation:
So we have the equation:
![|-4x+1|>3](https://tex.z-dn.net/?f=%7C-4x%2B1%7C%3E3)
First, note that since the sign is greater than, this is an <em>or</em> inequality (not an "and" inequality). This is the student's first mistake.
So, let's solve this inequality.
Case 1:
![-4x+1>3](https://tex.z-dn.net/?f=-4x%2B1%3E3)
Subtract 1 from both sides:
![-4x>2](https://tex.z-dn.net/?f=-4x%3E2)
Divide both sides by -4:
![x](https://tex.z-dn.net/?f=x%3C-%5Cfrac%7B1%7D%7B2%7D)
The student did not flip the sign when doing this step, hence the incorrect answer.
You correctly spotted the student's mistake. Nicely done!
Case 2:
![-4x+1](https://tex.z-dn.net/?f=-4x%2B1%3C-3)
This is what you're missing: for this second instance, we <em>must</em> flip the sign to <em>less than</em> right away. This is because we are essentially multiplying the 3 by a negative. So, we must flip the sign in order to be correct.
Now solve. Subtract 1 from both sides:
![-4x](https://tex.z-dn.net/?f=-4x%3C-4)
Divide both sides by -4. Since we're dividing by a negative, flip the sign:
![x>1](https://tex.z-dn.net/?f=x%3E1)
So, our solutions are:
![x1](https://tex.z-dn.net/?f=x%3C-%5Cfrac%7B1%7D%7B2%7D%2C%20x%3E1)
As mentioned previously, this is an <em>or</em> inequality. Therefore, our final answer is:
![x1](https://tex.z-dn.net/?f=x%3C-%5Cfrac%7B1%7D%7B2%7D%5Ctext%7B%20or%20%7D%20x%3E1)
Edit: Improved Answer
The answer should be 50 calories in each serving of vegetables.
Answer:
what do u want to talk about
Step-by-step explanation:
<u>First remove:</u>
Probability of removing a trained rat is 6/8
Probability of removing untrained rat is 2/8
Outcome is 6/8 + 2/8 = 1
<u>Second remove:</u>
Probability of picking a trained rat is 5/7
Probability of picking untrained rat is 1/7
Outcome is 6/7
<u>Third remove:</u>
Outcome is 1 (Since you can only remove a trained rat)
<u>Forth remove:</u>
Outcome is 1 (Since you can only remove a trained rat)
<u>Fifth remove:</u>
Outcome is 1 (Since you can only remove a trained rat)
Total outcome = 1 + 6/7 + 1 + 1 + 1 = 34/7 = 4(6/7)