Question

solve for v and graph the solution.
6 > |v - 15| - 9
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 \( 6 > |v - 15| - 9 \). Add 9 to both sides to isolate the absolute value expression:
\( 6 + 9 > |v - 15| \)
\( 15 > |v - 15| \)

Step2: Rewrite as compound inequality

Recall that \( |x| < a \) (for \( a > 0 \)) is equivalent to \( -a < x < a \). Here, \( a = 15 \) and \( x = v - 15 \), so:
\( -15 < v - 15 < 15 \)

Step3: Solve for \( v \)

Add 15 to all parts of the compound inequality:
\( -15 + 15 < v - 15 + 15 < 15 + 15 \)
\( 0 < v < 30 \)

Answer:

The solution for \( v \) is \( 0 < v < 30 \). To graph this, draw a line segment on the number line between \( 0 \) and \( 30 \), with open circles at \( 0 \) and \( 30 \) (since the inequality is strict, \( v \) does not equal \( 0 \) or \( 30 \)) and the segment connecting them.