Question

Please solve this question and show your work! Thank you!

Answer 1

`u<-1\text{ or } u>2`

Explanation:

So we have the equation:

`-3|2-4u|+5<-13`

First, subtract -5 from both sides:

`-3|2-4u|<-18`

Divide both sides by -3. Since we are dividing by a negative, we will flip the sign:

`|2-4u|>6`

Definition of absolute value:

`2-4u>6\text{ or } 2-4u<-6`

Note that we flip the sign on the right because we multiplied 6 by a negative.

On both the left and right, subtract 2:

`-4u>4\text{ or } -4u<-8`

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

`u<-1\text{ or } u>2`

So, our final solution is:

`u<-1\text{ or } u>2`

And we're done!