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In $3-38,$ solve each equation for the variable, check, and write the solution set.$$2+\sqrt[3]{3 b-2}=6$$

$\{22\}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 8

Solving Radical Equations

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

00:48

In $3-38,$ solve each equa…

02:41

04:15

00:43

02:48

05:57

02:29

06:13

00:35

02:23

you have the equation here. Two plus the Q groot of three B minus two is equal to six. That's first, and let's go and subtract two from both sides of the equation to just isolate our cube root. So subtracting two from both sides just leaves the while the cube root off three B minus two is gonna be equal to six minus two, which is equal to on four. Right? Okay, then, while we can go ahead and we can cube both sides of the equation here too, then eliminate the cube root. So if we if we cube if we cube the left side what we get me a three beat the cube root of three B minus four Cube is just gonna be equal to three B minus two. And then if we cube the right side, get four cube. So that is four times four times four, which is 64 right, four times for 16 time. Forget 64. So get three B minus two is quote shoes 64. Okay, so I just have a linear equation. Weaken go in ad to Tebow size to isolate RP term. So we have the three B is equal to 64 plus two over adding to the both sides here. That's equal to 66. And then we just go ahead and divide through by three. Right? Just be over. Three is one that is going to be is equal to 66/3 and 66. Divided by three is equal to 22. So that be is equal to 22. Does that check out while B is 22? We have two plus. The cube root of three times 20 to minus two should be equal to six. So we have not two times. Two plus me. Right. So, um, is this true? Well, we get two plus the cube root of three times 22. So that's, um, 66. Right? Minus two is 64 the cube root of 64 which is for right. So we get that two plus again. The Cuba of 54 years forced me. A two plus four is equal to six. Is that true? Yes, you've got six is equal to six, so it checks out and we get that be equal. 22 is about a solution. So therefore, our solution set is the set containing 22. All right,

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