Question

solve for d and graph the solution.
|d - 985| ≥ 10
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.
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950 955 960 965 970 975 980 985 990
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Explanation:

Step1: Split absolute - value inequality

For \(|d - 985|\geq10\), we have two cases: \(d - 985\geq10\) or \(d - 985\leq - 10\).

Step2: Solve the first case

Solve \(d - 985\geq10\). Add 985 to both sides: \(d\geq10 + 985\), so \(d\geq995\).

Step3: Solve the second case

Solve \(d - 985\leq - 10\). Add 985 to both sides: \(d\leq-10 + 985\), so \(d\leq975\).

Answer:

The solution is \(d\leq975\) or \(d\geq995\). On the number - line, there will be a ray starting from 975 (filled - in circle) going to the left and a ray starting from 995 (filled - in circle) going to the right.