Question

Show that if |x + 3| < 1/2, then |4x + 13| < 3.

I have no idea how to do this. I thought I might have to use the triangle inequality thing but that got me no where

for the first equation I got a soultion of

(-7/2, -5/2)

and for the second soultion i got

(-4, -5/2)

I thought it was interesting that the upper end points on both were the same but the beggining differ by half in magnitude so I don't know how to do this problem if you could show me that would be great thanks

Answer 1

We know that x is between -7/2 and -5/2
If x = -7/2, what is |4x+13|? answer 2
If x = -5/2, what is |4x+13|? answer 3