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# help with inequality

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Find all integers n such that $$2n < n - 4 \le 3n + 8$$

Jul 29, 2020

#1
+1042
+6

Solving directly for n is pretty hard. Which is why we can divide this up into two inequalities:

$$2n and \(n-4\leq3n+8$$

Let's solve the first one:

$$2n \(\text{Subtract n from both sides}$$

$$n<-4$$

Now, let's solve the second one:

$$n-4\leq3n+8$$

$$\text{Subtract n from both sides}$$

$$-4\leq2n+8$$

$$\text{Subtract 8 from both sides}$$

$$-12\leq2n$$

$$\text{Divide by 2}$$

$$-6\leq n$$

So, our inequality is now:

$$-6 \leq n < -4$$

Therefore, the integer solutions are:

$$\boxed{-6, -5}$$

Jul 29, 2020
edited by ilorty  Jul 29, 2020
#2
+1042
+6

It seems that my LaTeX has not loaded properly. Wherever it says \(2n, I mean 2n < n-4

ilorty  Jul 29, 2020