Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 230

solve the inequalty

solve the inequalty

where b is real parameter

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: solve the inequalty

If b = 0, we have |x| < 0, which is not possible. So either b > 0 or b < 0.

Consider first the case

Then the graph of

is a V shape with the vertex on the x-axis to the left of the origin and

is a positively sloped straight line passing through the origin. If

the slope of the latter is not greater than the slope of the right arm of the V (where

); hence the two curves will never intersect, and we would always have

So in this case we must have

then

Now consider the case

In this case, the vertex of

is to the right of the origin and

is still pssitively sloped passing through the origin; hence, this time the latter will always intersect the left arm of the V (where

).

Then

again.

So the solution is

tony123

Member

Registered: 2007-08-03

Posts: 230

Re: solve the inequalty

nice JaneFairfax

thank you