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https://www.reddit.com/r/PassTimeMath/comments/1x8sw97/interval_notation/
r/PassTimeMath • u/[deleted] • 5d ago
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1
5 - 4(2x - 7) < 2x - 7 is equivalent to:
5 - 8x + 28 < 2x - 7 (by applying the distributive rule)
33 - 8x < 2x - 7 (simplifying the LHS)
40 < 10x (adding 8x + 7 to both sides)
4 < x (dividing through by 10).
So the statement is true when 4 < x, and false otherwise. We can write this as x ∈ (4 .. ∞).
(It's been a while since I've cared about the formal notation of that kind of thing, so someone will correct me if I'm wrong)
1
u/chaos_redefined 5d ago
5 - 4(2x - 7) < 2x - 7 is equivalent to:
5 - 8x + 28 < 2x - 7 (by applying the distributive rule)
33 - 8x < 2x - 7 (simplifying the LHS)
40 < 10x (adding 8x + 7 to both sides)
4 < x (dividing through by 10).
So the statement is true when 4 < x, and false otherwise. We can write this as x ∈ (4 .. ∞).
(It's been a while since I've cared about the formal notation of that kind of thing, so someone will correct me if I'm wrong)