Question

solve for d and graph the solution.
2 < |d - 26|
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.
number line with 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34 marked

Explanation:

Step1: Recall absolute value inequality rule

For \(|x|>a\) (where \(a > 0\)), the solution is \(x < -a\) or \(x > a\). Here, our inequality is \(2<|d - 26|\), which is equivalent to \(|d - 26|>2\). So we can split this into two inequalities:
\(d - 26 < - 2\) or \(d - 26>2\)

Step2: Solve \(d - 26 < - 2\)

Add 26 to both sides of the inequality:
\(d-26 + 26<-2 + 26\)
\(d<24\)

Step3: Solve \(d - 26>2\)

Add 26 to both sides of the inequality:
\(d-26 + 26>2 + 26\)
\(d>28\)

Answer:

The solution for \(d\) is \(d < 24\) or \(d>28\). To graph this, we draw an open circle at 24 (since \(d\) is not equal to 24) and an arrow pointing to the left (for \(d < 24\)), and an open circle at 28 (since \(d\) is not equal to 28) and an arrow pointing to the right (for \(d>28\)) on the number line.