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.
<---22---23---24---25---26---27---28---29---30---31---32---33---34--->

Explanation:

Step1: Recall absolute value inequality rule

For \( |x| > a \) (where \( a>0 \)), it is equivalent to \( x > a \) or \( x < -a \). So for \( 2 < |d - 26| \), we can rewrite it as \( |d - 26|>2 \), which means \( d - 26>2 \) or \( d - 26 < - 2 \).

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

Add 26 to both sides: \( d-26 + 26>2 + 26 \), so \( d>28 \).

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

Add 26 to both sides: \( d-26+26 < - 2 + 26 \), so \( d < 24 \).

Answer:

The solution for \( d \) is \( d < 24 \) or \( d>28 \). To graph it, we use open circles at 24 and 28. Draw an arrow to the left from 24 (since \( d < 24 \)) and an arrow to the right from 28 (since \( d>28 \)).