If x 8 lessthanorequalto 9 then a lessthanorequalto 2x 6 le

If |x +8| lessthanorequalto 9, then a lessthanorequalto 2x - 6 lessthanorequalto b. Find a and b. a = (Simplify your answer.)

Solution

If I x +8 I 9 , then - 9 x + 8 9 or, -17 x 1 . Now, if a 2x -6 b, then (a+6) 2x    (b+6) or, (a+6)/2 x (b+6)/2 Thus, (a+6)/2 = -17 and (b+6)/2 = 1 so that a = -34 -6 = -40. and b = 2 -6 = - 4.