Question

solve the following compound inequality. write the solution set using interval notation and graph it.
$\frac{1}{3}(x + 2)>3$ or $0<5 - x$
select the correct choice below, and fill in the answer box if necessary.
a. the solution set is $(-\infty,5)\cup(7,\infty)$.
(type your answer in interval notation. simplify your answer. use integers or fractions for any numbers in the expression.)
b. the solution set is $\varnothing$.
choose the correct graph below.

Explanation:

Step1: Solve $\frac{1}{3}(x + 2)>3$

Multiply both sides by 3: $x+2>9$. Then subtract 2 from both sides: $x > 7$.

Step2: Solve $0<5 - x$

Add $x$ to both sides: $x<5$.

Step3: Combine solutions

Since it is an "or" compound - inequality, the solution set is the union of the two solution sets. The solution set in interval notation is $(-\infty,5)\cup(7,\infty)$.

Answer:

A. The solution set is $(-\infty,5)\cup(7,\infty)$.
The correct graph is A as it shows an open - circle at 5 with an arrow pointing to the left and an open - circle at 7 with an arrow pointing to the right.