The solution to the inequality, |v + 3| ≤ 3 is v ≤ 0 or v ≥ -6, and is shown below in the graph.
How to solve an inequality?
To solve the inequality |v + 3| ≤ 3, we can consider two cases:
1. When v + 3 is non-negative ( v + 3 ≤ 0 ):
v + 3 ≤ 3
Solving for v:
v ≤ 0
2. When v + 3 is negative (v + 3 < 0):
-(v + 3) ≤ 3
Solving for v:
-v - 3 ≤ 3
-v ≤ 6
v ≥ -6
So, combining both cases, the solution to |v + 3| ≤ 3 is v ≤ 0 or v ≥ -6. The graph is shown below.