Question

solve for t and graph the solution.
|t - 7| ≥ 2
click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or
two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles,
click on them.

Explanation:

Step1: Solve the absolute - value inequality

Given \(|t - 7|\geq2\). By the definition of absolute value, if \(|x|\geq a\) (\(a\geq0\)), then \(x\geq a\) or \(x\leq - a\).
For \(|t - 7|\geq2\), we have \(t-7\geq2\) or \(t - 7\leq-2\).

Step2: Solve \(t-7\geq2\)

Add 7 to both sides of the inequality \(t-7\geq2\).
\(t-7 + 7\geq2+7\), so \(t\geq9\).

Step3: Solve \(t - 7\leq-2\)

Add 7 to both sides of the inequality \(t - 7\leq-2\).
\(t-7 + 7\leq-2 + 7\), so \(t\leq5\).

Answer:

The solution of the inequality \(|t - 7|\geq2\) is \(t\leq5\) or \(t\geq9\). To graph the solution:

• For \(t\leq5\), we draw a ray starting at \(t = 5\) (with a filled - in circle since the inequality is \(\leq\)) and extending to the left.
• For \(t\geq9\), we draw a ray starting at \(t = 9\) (with a filled - in circle since the inequality is \(\geq\)) and extending to the right.