Consider u = {x|x is a real number}.
a = {x|x ∈ u and x + 2 > 10}
b = {x|x ∈ u and 2x > 10} which statements are true?

a. 5 ∉ a; 5 ∈ b

b. 6 ∈ a; 6 ∉ b

c. 8 ∉ a; 8 ∈ b

d. 9 ∈ a; 9 ∉ b

The given inequality for set A is :

x + 2 > 10

Next step is to subtract 2 from each sides of the inequality to isolate x.

So, x + 2 - 2 > 10 -2

x > 8

x is greater than 8 means the set of values of A is { 9, 10, 11, 12 ,..........}

Similarly let's solve the second inequality now. So,

2x > 10

Divide each sides by 2.

So, x > 5.

Hence, the set of values of B is { 6, 7, 8, 9, 10, 11, 12,................}

Now from the attach diagram notice that C. 8 ∉ A; 8 ∈ B is correct.

Hope this helps you!

answer: (3,11) is your answer.

the correct answer is 1.7