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

We know that if \(|x|\geq a\) (\(a > 0\)), then \(x\geq a\) or \(x\leq - a\). So for \(|d - 985|\geq10\), we have \(d-985\geq10\) or \(d - 985\leq - 10\).

Step2: Solve \(d-985\geq10\)

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

Step3: Solve \(d - 985\leq - 10\)

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

Answer:

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