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.

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 of the inequality by - 6. When multiplying or dividing 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 $(-\infty,-6)$.
To graph this on a number line, we draw an open - circle at $x=-6$ (because $x$ cannot equal - 6) and draw an arrow to the left to represent all the values less than - 6.

Answer:

The solution set in interval notation is $(-\infty,-6)$. The correct graph is the one with an open - circle at $-6$ and an arrow pointing to the left, which is likely option A (assuming option A has this correct graph representation).