Question

solve for d and graph the solution. -1 > |d - 32| - 2 click two endpoints to graph a line segment, an endpoint and ray, or two arrowheads to graph a line. to change endpoints from circles, click on them.

Explanation:

Step1: Isolate the absolute value expression

Start with the inequality \(-1 > |d - 32| - 2\). Add 2 to both sides to isolate the absolute value term.
\[
-1 + 2 > |d - 32| - 2 + 2
\]
\[
1 > |d - 32|
\]
Which is equivalent to \(|d - 32| < 1\).

Step2: Solve the absolute value inequality

Recall that \(|x| < a\) (where \(a>0\)) is equivalent to \(-a < x < a\). So for \(|d - 32| < 1\), we have:
\[
-1 < d - 32 < 1
\]

Step3: Solve for \(d\)

Add 32 to all parts of the compound inequality:
\[
-1 + 32 < d - 32 + 32 < 1 + 32
\]
\[
31 < d < 33
\]

Answer:

The solution for \(d\) is \(31 < d < 33\). To graph this, we would draw a line segment on the number line with open circles at 31 and 33 (since the inequality is strict, not including the endpoints) and the segment between them.