Question

which graph represents the solution set to the following inequality?\\(\frac{x - 6}{2} > 3\\)\
(first number line: open circle at 12, arrow to the left; options with 0,2,4,6,8,10,12,14)\
(second number line: open circle at 12, arrow to the right)\
(third number line: open circle at 2, arrow to the left)\
(fourth number line: open circle at 2, arrow to the right)\
scientific calculator

Explanation:

Step1: Solve the inequality

To solve \(\frac{x - 6}{2}>3\), multiply both sides by 2 (since 2 is positive, the inequality sign remains the same):
\(x - 6>3\times2\)
\(x - 6>6\)

Step2: Isolate \(x\)

Add 6 to both sides:
\(x>6 + 6\)
\(x>12\)

Step3: Analyze the number line

The solution \(x > 12\) means an open circle at 12 (since 12 is not included) and an arrow pointing to the right (for values greater than 12). Looking at the options, the second graph (with open circle at 12 and arrow right) matches.

Answer:

The second graph (the one with open circle at 12 and arrow pointing to the right, labeled with 0, 2, 4, 6, 8, 10, 12, 14 on the number line).