4-3x <=0 and x + 5 > 0 (Why is one inequality strict and one not?)
4 - 3x >= 0 and x + 5 <0
Each part starts out as the intersection of two intervals, which combine into a single interval. For example, the first part gives you [4/3,infinity) and (-5,infinity), which intersect to [4/3, infinity)
The second part gives you (-infinity,4/3] and (-infinity, -5), which intersect to (-infinity, -5).
The final answer is the union of the answers to each part.
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Well, there are two possibilities:
4-3x <=0 and x + 5 > 0 (Why is one inequality strict and one not?)
4 - 3x >= 0 and x + 5 <0
Each part starts out as the intersection of two intervals, which combine into a single interval. For example, the first part gives you [4/3,infinity) and (-5,infinity), which intersect to [4/3, infinity)
The second part gives you (-infinity,4/3] and (-infinity, -5), which intersect to (-infinity, -5).
The final answer is the union of the answers to each part.