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}{6}>4
a. the solution set in interval notation is (-\infty,-6.
(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. graph with arrow pointing left and ending at - 6
b. graph with arrow pointing right and starting at 6
c. graph with arrow spanning from - 10 to 10
d. graph with arrow pointing left and ending at - 4
e. graph with arrow pointing right and starting at 6
f. the solution set is \\(\varnothing\\).

Explanation:

Step1: Isolate the variable term

Subtract 3 from both sides of the inequality $3-\frac{x}{6}>4$:
$3 - \frac{x}{6}-3>4 - 3$
$-\frac{x}{6}>1$

Step2: Solve for x

Multiply both sides by - 6. When multiplying an inequality by a negative number, the direction of the inequality sign changes.
$(-6)\times(-\frac{x}{6})<1\times(-6)$
$x < - 6$
In interval - notation, the solution set is $(-\infty,-6)$.

Answer:

The solution set in interval notation is $(-\infty,-6)$. The correct graph is a number - line with an open circle at - 6 and an arrow pointing to the left. Among the given options, if option A has an open circle at - 6 and an arrow pointing to the left, then the answer for the graph part is A.