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Solve |5 + 3w| <= 2.

 Sep 9, 2020
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We have 2 cases, \(5 + 3w \le 2, and -5 - 3w \le 2\)

 

Starting with the first case \(​​5 + 3w \le 2\) , we can subtract 5 from both sides to get \(3w \le -3\), and then divide by 3 for an answer of \(w \le -1\), keeping in mind 3 is positive so we don't switch the sign.

 

Now for our second case, \(- 5 - 3w \le 2\), we add five to both sides giving us, \(- 3w \le 7\), now dividing by \(-3\) and making sure we flip the sign, we get, 

\(w \ge - \dfrac{7}{3}\)

 

But wait, we still have to combine our answers giving us \(\boxed{-\frac{7}{3} \le w \le -1}\)

 Sep 9, 2020

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