Question

please help i don't understand how to do this

Answer 1

hey @jim_thompson5910 can you help me out please? :)

Answer 2

When you have an absolute value, there is two possibilities for the value between the absolute sign. It will be either the positive of the value between the absolute sign or negative of the value between the absolute sign.

In your inequality, you have the absolute value of 4x +1. So the positive of that value is just 4x +1. However, you also have the negative of 4x + 1, written like this: -(4x +1).

So now you just solve the inequality once for the positive value and once for the negative value.

So for the positive value, you remove the absolute sign and your inequality looks like this:\[4x +1 < 5\]\[4x <5-1\]\[x <4/4\]\[x <1\]

For the negative value, you take the negative of 4x +1 and your inequality looks like this:\[-1(4x+1)<5\]\[-4x -1<5\]\[-4x <5+1\]\[-4x <6\]\[x >6/-4\]Note when you multiply or divide by a negative number, you need to change the direction of the inequality sign.\[x >-3/2\]
So your answer is \[-3/2<x <1\]

Answer 3

oh wow thank you very much! :)