Question

Please Please help! I am so beyond stuck. I have figured out what is wrong with the first step but I cant figure out what is going on with the second one!

Answer 1

`x<-(1)/(2)\text{ or } x>1`

Explanation:

So we have the equation:

`|-4x+1|>3`

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:

`-4x+1>3`

Subtract 1 from both sides:

`-4x>2`

Divide both sides by -4:

`x<-(1)/(2)`

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<-3`

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:

`-4x<-4`

Divide both sides by -4. Since we're dividing by a negative, flip the sign:

`x>1`

So, our solutions are:

`x<-(1)/(2), x>1`

As mentioned previously, this is an or inequality. Therefore, our final answer is:

`x<-(1)/(2)\text{ or } x>1`

Edit: Improved Answer