Question

Given that 1/(x-3)>5/8 which of the following can be the value of x ? (A) 16/5 (B) 12/5 (C) 2 (D) 8/9 (E) 4/5​

Answer 1

Step-by-step explanation:

1/(x-3) > 5/8 means 1/(x-3) is positive which means x-3 is positive.

hence, x-3 >0 ➡ x>3 ..... eq (1)

Also, since x-3 is positive we can multiply by (x-3) both sides.

so,

➡(x-3)/(x-3) > 5*(x-3)/8

➡1 > 5*(x-3)/8

➡ 8/5 > x-3

➡ 23/5 > x ..... eq (2)

from equation (1) and (2), we can conclude that

3< x < 23/5 ➡ 15/5 < x < 23/5 ( since 3 =15/5)

so, from the options, only 16/5 can be valid since it lies between 15/5 and 23/5 and all other options are not valid.

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