Solve the inequalities write your answers in interval notati

Solve the inequalities, write your answers in interval notation:

Solution

a) (1 + x)/ (1 - x) 1 or, 1 + x 1 - x or, 2x 1 -1 or 2x 0 or x 0. However, x can not be 1 as then 1 - x = 0 and division by 0 is not defined. Thus x 0, but x 1. Also x can not be > 1 for then the denominator !-x will be negative and then (1+x)/ ( 1-x) will be negative i.e. < 0 and hence < 1 . Thus the answer is [ 0, 1)

b) 0 < mod (x ) 99 . mod (x) will always be greater that 0 unless x = 0. Since 0 < mod (x), x 0.. Also mod (x) 99 means that either x > 0 and x 99 or x < 0 and x - 99.Hence, the answer is [ -99, 0 ) U ( 0, 99]