Question

solve for t and graph the solution.
t - 6 ≤ 5 or t - 18 ≥ - 2
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Explanation:

Step1: Solve the first inequality

Add \(6\) to both sides of \(t - 6\leq5\).
\(t-6 + 6\leq5 + 6\), so \(t\leq11\).

Step2: Solve the second inequality

Add \(18\) to both sides of \(t - 18\geq - 2\).
\(t-18 + 18\geq - 2+18\), so \(t\geq16\).

Answer:

The solution of the compound inequality \(t - 6\leq5\) or \(t - 18\geq - 2\) is \(t\leq11\) or \(t\geq16\). On the number - line, we place a closed circle at \(t = 11\) (since \(t = 11\) is included in \(t\leq11\)) and shade to the left of \(11\), and place a closed circle at \(t = 16\) (since \(t = 16\) is included in \(t\geq16\)) and shade to the right of \(16\).