Math trouble, simple question please help?

Question

Now I was doing my home-school and this question blew me out of my mind.

a+2 < b+3, then a < b.

The correct awnser was FALSE.

Now how can a+2 be less than b+3... but not be less then b?

So why would a < b, then a+2 < b +3 would be concidered true???? (Not totaly sure)

Answer 1

b can be 0 and lets say that a can be .5

.5 +2 &lt; 0 + 3    

Answer 2

if a = -3   -3 +2 = -1  

if b = -3   -3+3=  0

-3 + 2 &lt; -3 + 3

-1         &lt;  0

Answer 3

Suppose a=b. Then a+2 &lt; b+3, but a is not less than b.

Answer 4

its because a can be equal to b so when it says than a&lt;b it can be false

For example:

if a would = 4

and b would = 4

then that means that the equation would be like this  4 + 2 &lt; 4 + 3 which is true and in the equation a and be are equal so that statement that said a &lt; b is untrue because it could also be equal to it

hopethat wasnt confusing and also hope it helped

Answer 5

a+2 &lt; b+3, then a &lt; b

a+2 -2 &lt; b+3 -2

a &lt; b + 1

a-b &lt; b + 1 - b

a-b &lt; 1

a - b &lt; 1 if

1) a &lt; b

2) a = b

3) a &lt;  b + 1, in this case a &gt; b

so, it is true in all cases thus the conclusion is false

Answer 6

If you subtract 2 from both sides of the inequality, you get a &lt; (b + 1), from which it may be seen that a may be greater than b but less than b + 1