@electricalmath: Absolute value inequalities can be tricky, so let’s have a look at a methodical approach you can use when solving such problems. In partnership with Mathos AI. Check out this powerful AI solver using the link in my bio. #math
Since the expressions within the absolute values are linear, there is a much easier way.
g(x)=|x-3|+|x+2| is piecewise linear and can only change its behavior at 3 and -2.
So calculate g(-2), g(3) and g(x) for an x lt -2 and an x gt 3:
g(-3)=7, g(-2)=5, g(3)=5, g(4)=7
So, the graph of g looks like \_/ with the corners at -2 and 3, while
g(x)=5-2(x+2) for x lt -2
g(x)=5+2(x-3) for x gt 3
Solving g(x)=11 for these two cases gives immediately
x in (-5,6)
2025-11-16 10:09:52
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