Answer:
[tex]x<-\frac{1}{2}\text{ or } x>1[/tex]
Step-by-step explanation:
So we have the equation:
[tex]|-4x+1|>3[/tex]
First, note that since the sign is greater than, this is an or inequality (not an "and" inequality). This is the student's first mistake.
So, let's solve this inequality.
Case 1:
[tex]-4x+1>3[/tex]
Subtract 1 from both sides:
[tex]-4x>2[/tex]
Divide both sides by -4:
[tex]x<-\frac{1}{2}[/tex]
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:
[tex]-4x+1<-3[/tex]
This is what you're missing: for this second instance, we must flip the sign to less than 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:
[tex]-4x<-4[/tex]
Divide both sides by -4. Since we're dividing by a negative, flip the sign:
[tex]x>1[/tex]
So, our solutions are:
[tex]x<-\frac{1}{2}, x>1[/tex]
As mentioned previously, this is an or inequality. Therefore, our final answer is:
[tex]x<-\frac{1}{2}\text{ or } x>1[/tex]
Edit: Improved Answer
