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

• A. $\left(-\infty,\frac72\right)$
• B. $\left(-\infty,\frac72\right]$
• C. $\left[\frac72,\infty\right)$
• D. $\left(\frac72,\infty\right)$

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 get \(2x > 7\).
2. Next, divide both sides of the inequality by 2 to solve for \(x\). This gives \(x > \frac{7}{2}\).
3. Express the solution set in interval notation. Since \(x\) is greater than \(\frac{7}{2}\), the interval notation is \((\frac{7}{2}, \infty)\).
4. To graph the solution, draw a number line. Mark \(\frac{7}{2}\) on the number line and use an open circle to indicate that \(\frac{7}{2}\) is not included in the solution set.
5. Shade the region to the right of \(\frac{7}{2}\) to represent all values greater than \(\frac{7}{2}\). This visualizes the solution \((\frac{7}{2}, \infty)\).