Question

solve for d and graph the solution.
|d - 775| - 1 ≤ 24
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.

Explanation:

Step1: Isolate the absolute value

Start with the inequality \(|d - 775| - 1 \leq 24\). Add 1 to both sides:
\(|d - 775| \leq 24 + 1\)
\(|d - 775| \leq 25\)

Step2: Solve the absolute value inequality

The absolute value inequality \(|x| \leq a\) (where \(a \geq 0\)) is equivalent to \(-a \leq x \leq a\). Here, \(x = d - 775\) and \(a = 25\), so:
\(-25 \leq d - 775 \leq 25\)

Step3: Solve for \(d\)

Add 775 to all parts of the compound inequality:
\(-25 + 775 \leq d - 775 + 775 \leq 25 + 775\)
\(750 \leq d \leq 800\)

Answer:

The solution for \(d\) is \(750 \leq d \leq 800\). To graph this, plot a line segment on the number line with filled - in circles at 750 and 800 (since the inequality is "less than or equal to") and the segment connecting them.