Question

solve the inequality and graph the solution.
3(t + 2) ≥ 12
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 \(a(b + c)=ab+ac\). So \(3(t + 2)=3t+6\), and the inequality becomes \(3t + 6\geq12\).

Step2: Isolate the term with \(t\)

Subtract 6 from both sides of the inequality: \(3t+6 - 6\geq12 - 6\), which simplifies to \(3t\geq6\).

Step3: Solve for \(t\)

Divide both sides of the inequality by 3: \(\frac{3t}{3}\geq\frac{6}{3}\), so \(t\geq2\).

Answer:

The solution of the inequality is \(t\geq2\). On the number - line, you would plot a closed circle at \(t = 2\) (because the inequality is \(\geq\)) and draw a ray to the right of 2.