Answer: 5 > k
Step-by-step explanation: When you're asked to solve an inequality like -45 < -9k, your goal should be the same as it was when solving equations which is to get <em>k</em> by itself on one side.
In this problem since <em>k</em> is being multiplied by -9 on the right side of the inequality, to get <em>k</em> by itself, we divide both sides by -9 but here is the rule you have to watch out for when solving inequalities.
When you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign. So this less than in our original problem becomes greater than in our second step. I would recommend switching it as soon as possible so you don't forget.
Let's rewrite our original inequality.
-45 < -9k
On the right side, the -9's cancel and we're left with <em>k</em> and on the right side, -45 divided -9 is -5. So we have <em>5 </em><em>></em><em> k</em>.
![x^{\frac{m}{n}}=\sqrt[n]{x^{m}}](https://tex.z-dn.net/?f=%20x%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D%3D%5Csqrt%5Bn%5D%7Bx%5E%7Bm%7D%7D%20)
![[3(2a)^{\frac{3}{2}}]^{2}](https://tex.z-dn.net/?f=%20%5B3%282a%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5D%5E%7B2%7D%20)
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