If |x + 3| < 1/ 2 , determine whether the statement |4x + 13| < 3 is true or false.

Question

I've solved for both and I know that for |x+3| < 1/2 , x lies on the interval of (-3.5, -2.5)

 

For |4x+13| < 3, x lies on (-4, -2.5) 

 

Is the statement true or false?

 

thanks in advance

Answer 1

|4x+13|=|4(x+3)+1|<=4|x+3|+1<4(1/2)+1=3.

Actually, it is rue.

Answer 2

the given absolute value inequality means -½ < x+3 < ½, so when we multiply by 4 we have

-2 < 4x+12 < 2.  we then add l and get

-1 < 4x+13 < 3...call this FACT 1. 

 

comparing this to question -3 < 4x+13 < 3, which is equivalent to |4x+13| < 3, we see that SOME VALUES THAT SATISFY THE QUESTION WOULD BE OUTSIDE THE INTERVAL OF TRUTH BASED ON FACT 1.

 

FALSE!