Question

this question has two parts. first, answer part a then, answer part b
part a
solve the inequality ( 80 geq - 5 t ) and write the solution in set - builder notation.
part b
graph the solution on a number line.

Explanation:

Step1: Solve the inequality

Given \(80\geq - 5t\).
Divide both sides by \(-5\). When dividing an inequality by a negative number, the direction of the inequality sign changes. So we have \(\frac{80}{-5}\leq t\), which simplifies to \(t\geq - 16\).
In set - builder notation, this is \(\{t|t\geq - 16\}\).

Step2: Graph the solution on the number line

The solution \(t\geq - 16\) means we have a closed circle at \(-16\) (because the inequality includes equality, i.e., \(t = - 16\) is part of the solution) and an arrow pointing to the right (towards larger values of \(t\)).

Answer:

• Part A: The solution in set - builder notation is \(\{t|t\geq - 16\}\).
• Part B: The correct graph is option B (assuming option B has a closed circle at \(-16\) and an arrow to the right).