Question

solve for u and graph the solution.
25 ≤ |u - 880|
click two endpoints to graph a line segment, an endpoint and an arrow ray, or two arrowheads to graph a line. to change endpoints from filled - in circles, click on them.
855 860 865 870 875 880 885 890 895 900 905
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Explanation:

Step1: Recall absolute value inequality rule

The inequality \(|x| \geq a\) (where \(a>0\)) is equivalent to \(x \geq a\) or \(x \leq -a\). So for \(25 \leq |u - 880|\), we can rewrite it as \(|u - 880| \geq 25\), which means \(u - 880 \geq 25\) or \(u - 880 \leq - 25\).

Step2: Solve the first inequality

For \(u - 880 \geq 25\), add 880 to both sides:
\(u - 880+880 \geq 25 + 880\)
\(u \geq 905\)

Step3: Solve the second inequality

For \(u - 880 \leq - 25\), add 880 to both sides:
\(u - 880+880 \leq - 25+880\)
\(u \leq 855\)

Answer:

The solution for \(u\) is \(u \leq 855\) or \(u \geq 905\). To graph this, we would have a ray starting at 855 (with a filled - in circle) going to the left and a ray starting at 905 (with a filled - in circle) going to the right.