If y = 4x 3 and 0 < x < 3, then y is between
a) -3 & 9 b) -2 & 10 c) 0 & 12 d) 1 & 5 e) 1 & 9
The trick here is to build x into y, which is 4x - 3
by multiplying all three sides of
0 < x < 3
by 4 and then subtracting 3 from all three sides.
Multiplying all three sides of
0 < x < 3
by 4 gives:
4*0 < 4*x < 4*3
or
0 < 4x < 12
Now subtracting 3 from all three sides of the above
gives:
0 - 3 < 4x - 3 < 12 - 3
-3 < 4x - 3 < 9
And since y = 4x - 3, we can substitute y for 4x - 3
-3 < y < 9
and that says that y is between -3 and 9. Therefore
the correct choice is a)
Edwin