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In $3-38,$ solve each equation for the variable, check, and write the solution set.$$3-b=\sqrt{3 b-11}$$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 8

Solving Radical Equations

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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In $3-38,$ solve each equa…

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Okay, so we're going to solve this equation for be checker answers and then provide a solution set so unloved here we have through my speed, and we just square that because we'll square this side with the isolated radical. So I get when I do three minus b square, and I've got a foil that out. So three times three is nine of three times of minus. B is minus three B, and then another minus three gets B minus 60 and then a negative b times a negative. B is positive b squared. And so on the left, I'm going to just rearrange this here and then on the right. I get the three B minus 11 to get all of it over to the one side. I'm going to subtract three b and at 11 to both sides on the right. I'll get zero, cause all of that cancels up on the left. I'll get it B squared. A negative sex minus of three gets me a negative 90 plus 20. Now, when I factor this out, I get a B for the first term, and then I need in order to get a positive here and a negative for the second term. I've gotta have two negatives, and then the factors of 20 that add up to nine are four and five. So then solving for each of these I get that B is equal to four and B is equal to five. So let's test both of these out. In the original equation, I have three minus four, equal to the square root of three times four minus 11. And so three minus four is negative one and then I get a 12. Minus 11 is the square root of one, and a negative one is not equal to one. So let's also try this other number here, this five. So if I have three minus five, equal to the square root of three times five minus 11 I get three. Minus five is a negative two and then a five times of three 15. Minus 11 is the square root of four, and the negative, too, is not equal to two. So both of these do not work. And so the solution sat here is no

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