1.7 Solve \( \leftarrow \begin{array}{l}\text { Question 7, 1.7.35 } \\ \text { Part } 1 \text { of } 2 \\ \text { Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number } \\ 8(x+1)+2 \geq 7 x+17 \\ \text { Select the correct choice below and, if necessary, fill in the answer box to complete your choice. } 11 \\ \text { A. The solution is } \square \text {. (Type the solution using interval notation.) } \\ \text { B. The solution set is } \varnothing \text {. }\end{array} \) Save 1 .

To solve the inequality:   8(x + 1) + 2 ≥ 7x + 17 Step 1: Distribute and simplify the left-hand side.   8·x + 8·1 + 2 = 8x + 8 + 2 = 8x + 10 Now the inequality is:   8x + 10 ≥ 7x + 17 Step 2: Get all terms with x on one side by subtracting 7x from both sides.   8x + 10 – 7x ≥ 7x + 17 – 7x Simplify:   x + 10 ≥ 17 Step 3: Isolate x by subtracting 10 from both sides.   x + 10 – 10 ≥ 17 – 10 Simplify:   x ≥ 7 Thus the solution set in interval notation is: [7, ∞). Graphically, on the number line, shade all points starting at 7 (with a closed dot to indicate 7 is included) and extending to the right indefinitely. Select answer choice:   A. The solution is [7, ∞).