Which graph shows the solution set of 

Hence final answer is .

correct choice is D because both ends are open circles.

Step-by-step explanation:

Given inequality is

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:

, and

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

Test for .

Clearly x=0 belongs to interval then plug x=1 into

Which is False.

Hence desn't belongs to the answer.

Similarly testing other intervals, we get that only satisfies the original inequality.

Hence final answer is .

correct choice is D because both ends are open circles.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°