Which graph shows the solution set of

Question

asked Apr 9, 2020 229k views

1 Answer

Zurechtweiser · Answer 1 · 2020-04-16T07:49:16+0000

Answer:

Hence final answer is
(1,3) .

correct choice is D because both ends are open circles.

Explanation:

Given inequality is
(x-1)/(x-3)<0

Setting both numerator and denominator =0 gives:

x-1=0, x-3=0

or x=1, x=3

Using these critical points, we can divide number line into three sets:

$(-\infty,1)$ ,
(1,3) and
$(3,\infty)$

We pick one number from each interval and plug into original inequality to see if that number satisfies the inequality or not.

Test for
$(-\infty,1)$ .

Clearly x=0 belongs to
$(-\infty,1)$ interval then plug x=1 into
(x-1)/(x-3)<0

(0-1)/(0-3)<0

(-1)/(-3)<0

(1)/(3)<0

Which is False.

Hence
$(-\infty,1)$ desn't belongs to the answer.

Similarly testing other intervals, we get that only
(1,3) satisfies the original inequality.

Hence final answer is
(1,3) .

correct choice is D because both ends are open circles.