Solving inequalities with no solution or all real numbers as solutions For each inequality, choose the statement that describes its solution. If applicable, give the solution. \( \begin{array}{l}\text { (a) }-2(w+6)+19>2(5-w) \\ \text { No solution } \\ \text { All real numbers are solutions }\end{array} \)

Let's solve the inequality step by step to determine its solution. **Given Inequality:** \[ -2(w + 6) + 19 > 2(5 - w) \] **Step 1: Distribute the Constants** \[ -2w - 12 + 19 > 10 - 2w \] **Step 2: Combine Like Terms** \[ -2w + 7 > 10 - 2w \] **Step 3: Add \(2w\) to Both Sides** \[ -2w + 2w + 7 > 10 - 2w + 2w \] \[ 7 > 10 \] **Step 4: Analyze the Result** \[ 7 > 10 \] This statement is **false**. Since we've arrived at a falsehood, it means that there is no value of \(w\) that can satisfy the original inequality. **Conclusion:** - **Solution:** No solution. **Answer:** **No solution.** There is no real number \(w\) that satisfies the inequality.