Question

solve the inequality and graph the solution.
2(s + 2) - 3 ≥ 9
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Expand the left - hand side

Use the distributive property \(a(b + c)=ab+ac\).
\(2(s + 2)-3=2s+4 - 3=2s + 1\). So the inequality becomes \(2s+1\geq9\).

Step2: Isolate the term with \(s\)

Subtract \(1\) from both sides of the inequality.
\(2s+1-1\geq9 - 1\), which simplifies to \(2s\geq8\).

Step3: Solve for \(s\)

Divide both sides of the inequality by \(2\).
\(\frac{2s}{2}\geq\frac{8}{2}\), so \(s\geq4\).

Answer:

The solution of the inequality \(2(s + 2)-3\geq9\) is \(s\geq4\). On the number - line, we plot a closed circle at \(s = 4\) (because the inequality is \(\geq\)) and draw a ray to the right of \(4\).