Solve the inequality. Express the solution set in interval notation and graph. $2x+12>19$

• A. $\(\left\)(-\(\infty\),\(\frac\)72\(\right\))$
• B. $\(\left\)(-\(\infty\),\(\frac\)72\(\right\)]$
• C. $\(\left\)[\(\frac\)72,\(\infty\]\right\))$
• D. $\(\left\)(\(\frac\)72,\(\infty\]\right\))$

Answer: (D)

Verified step by step guidance

1. Start by isolating the variable on one side of the inequality. Given the inequality 2x + 12 > 19, subtract 12 from both sides to simplify the expression.
2. After subtracting 12 from both sides, the inequality becomes 2x > 7.
3. Next, divide both sides of the inequality by 2 to solve for x. This gives x > 7/2.
4. Express the solution set in interval notation. Since x is greater than 7/2, the interval notation is (7/2, ∞).
5. To graph the solution, draw a number line and mark an open circle at 7/2 to indicate that 7/2 is not included in the solution set. Shade the region to the right of 7/2 to represent all numbers greater than 7/2.