Question

other than a no - solution set, use interval notation to express the solution set and then graph the solution set on a number line. 3 - \frac{x}{2}>8. a. the solution set in interval notation is (-\infty, - 10 (simplify your answer. use integers or fractions for any numbers in the expression. type your answer in interval notation) b. the solution set is \\(\varnothing\\). graph the solution set on a number line. choose the correct graph below. a. number line graph with arrow pointing left b. number line graph with endpoint at 10 and arrow pointing right c. number line graph with endpoint at 10 and arrow pointing left d. number line graph with endpoint at - 10 and arrow pointing left e. number line graph with endpoint at - 10 and arrow pointing left f. the solution set is \\(\varnothing\\).

Explanation:

Step1: Isolate the term with x

Subtract 3 from both sides of the inequality $3-\frac{x}{2}>8$.
$3 - \frac{x}{2}-3>8 - 3$
$-\frac{x}{2}>5$

Step2: Solve for x

Multiply both sides by - 2. When multiplying an inequality by a negative number, the direction of the inequality sign changes.
$(-2)\times(-\frac{x}{2})<5\times(-2)$
$x < - 10$
In interval - notation, the solution set is $(-\infty,-10)$.

Answer:

A. The solution set in interval notation is $(-\infty,-10)$; E. (The graph that has an arrow pointing to the left starting from an open - circle at - 10 on the number line)