Question

ore algebra 1 b-cr
consider u = {x|x is a real number}.
a = {x|x ∈ u and x + 2 > 10}
b = {x|x ∈ u and 2x > 10}
which pair of statements is correct?
○ 5 ∉ a; 5 ∈ b
○ 6 ∈ a; 6 ∉ b
○ 8 ∉ a; 8 ∈ b
○ 9 ∈ a; 9 ∉ b

Explanation:

Step1: Simplify set A's condition

Solve $x + 2 > 10$:
$x > 10 - 2$
$x > 8$
So $A = \{x \in \mathbb{R} \mid x > 8\}$

Step2: Simplify set B's condition

Solve $2x > 10$:
$x > \frac{10}{2}$
$x > 5$
So $B = \{x \in \mathbb{R} \mid x > 5\}$

Step3: Test each option

• Option1: $5

otin A$ (true, $5
ot>8$); $5 \in B$ (false, $5
ot>5$) → Incorrect

• Option2: $6 \in A$ (false, $6

ot>8$); $6
otin B$ (false, $6>5$) → Incorrect

• Option3: $8

otin A$ (true, $8
ot>8$); $8 \in B$ (true, $8>5$) → Correct

• Option4: $9 \in A$ (true, $9>8$); $9

otin B$ (false, $9>5$) → Incorrect

Answer:

8 ∉ A; 8 ∈ B