Help with a math question?

Question

I dont understand why this problem can be done, my book got an answer for it. It is 1-|2-3x|<-4. I thought you can't have an absolute value equaling a negative. Is it doable only because you divide both sides by the -1 and it thus becomes a positive?

Answer 1

It makes it easier when both sides are positive. But it's doable if not too.

For your consideration
|x|>-4

This statement is true. It just tell us obvious stuff. The Important thing is that it's an inequality, not and equation.

Because
|x|= -4

Doesn't make sense.

Answer 2

Problem is 1-|2-3x| is less than -4.

This problem can be done.

Since you have "1-" out in front, you conclude that whatever is inside the absolute value brackets must must be less than 5. 1 minus 5 equals negative 4, but the inequlities states that the quantity must be less than -4.

So, |2-3x| must be less than positive 5 since you are subtracting this to get the solution to the inequality.

Therefore 2- 3(2) = 5.

We can conclude that x must be greater than 2 in order for the inequality to be true.

Answer 3

1-|2-3x|<-4

First, take the 1 to the opposite side.

-|2-3x| <-5

The "minus" sign in front of the absolute value is the same as multiplying by a -1.

Let's divide both sides by a negative 1.

|2-3x| > 5 (Remember the sign changes)

Now clear the absolute value sign as follows:

2-3x > 5 OR 2-3x < -5

Now solve:

-3x > 3 also -3x <-7

x > -1 also x < 7/3

So, the pair of inequalities here is the solution

Regards,

Mysstere

Answer 4

I think it goes like this -

1- (2-3x)<-4 =
1-2 +3x < -4 =
-1 +3x < -4 =
3x < -4 + 1 =
3x < -3 =
x < 1