Question

solve for t and graph the solution.
|9t - 495| - 6 < 219
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: Isolate the absolute value

Add \(6\) to both sides of the inequality \(|9t - 495|-6<219\).
\(|9t - 495|-6 + 6<219+6\)
\(|9t - 495|<225\)

Step2: Use the property of absolute - value inequalities

If \(|x|0\)), then \(-a < x < a\). Here \(x = 9t-495\) and \(a = 225\). So we have \(-225<9t - 495<225\).

Step3: Solve the compound inequality

Add \(495\) to all three parts of the compound inequality:
\(-225+495<9t-495 + 495<225+495\)
\(270<9t<720\)

Step4: Divide by \(9\)

Divide each part of the inequality \(270<9t<720\) by \(9\).
\(\frac{270}{9}<\frac{9t}{9}<\frac{720}{9}\)
\(30 < t<80\)

Answer:

The solution of the inequality is \(30 < t<80\). On the number - line, we click on the point \(30\) (make it an empty circle) and the point \(80\) (make it an empty circle) and then click between them to graph the line segment.