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# Inequality

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Solve 3t - 5 < t - 2 <= -3t + 7 - t + 8.  Give your answer as an interval.

Jun 7, 2022

#1
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$$3t-5 Adding \(4t$$ gives $$7t-5<5t-2\leq15$$.

Solving $$7t-5<5t-2$$ and $$5t-2\leq15$$ gives $$t<1.5$$ and $$t\leq3.4$$, respectively.

Combining these then shows that $$t<1.5$$, so therefore in interval notation the answer is $$(-\infty,1.5)$$.

Jun 7, 2022
#2
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Something went wrong with my Latex on line one, it's supposed to read \(3t-5 .

RainbowSquirrel53  Jun 8, 2022