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In $3-38,$ solve each equation for the variable, check, and write the solution set.$$1-\sqrt[3]{x+7}=4$$

$\{-34\}$

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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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one minus the cube root of X plus seven is equal to four. So first, let's go ahead and subtract one from both sides. Equation that would give us negative. The cube root of X plus seven is equal to while four minus one, attracting one from both sides equally. Three. Okay, then let's go ahead and just multiplied by a negative one to basically, we have a positive square room here. So if we do that, we get the square. The cube root excuse means to Cuba of X plus seven is gonna be then, while equal to negative three. So then, if we go ahead and cube both sides of the equation, right, the cube root of X plus seven cube just gives us experts seven. So eliminating the Q blue here. So we take the cube root of experts seven. And we cube it to just give us what's under the cube root under the radical, which it's just experts whips Whoops, which is just equal to X plus seven. Okay. And that's gonna be that equal to negative three Cube. So you have negative three times negative three, which is a positive nine. But then times negative three, which is negative. 27 negative. Three Cube is gonna be equal to a negative 27. Okay. In the south for X, we just go ahead and we subtract seven from both sides of the equation. Right. Linear equation. Now. So therefore, experts 7 May 27. Then there. Four x is equal to negative 27 minus seven, which is equal to negative 34. So therefore, access equal to negative 34. Now, if we go ahead and we check negative 34 as a solution, does that work? While negative 34 plus seven is gonna be equal to negative 27. And the cube root of negative 27 is negative three. So we have one minus a negative. Groups one hopes one minus one minus and negative in negative. Three should be equal to four because one minus the cube root again off negative. 30 47 is negative. 27 in the cube root of native 27 is negative. Three So one minus. The native three is one plus three, which is for so we check out to get forwards equal before therefore, our solution is valid in our solution. Set here is the sets containing well, negative 34. All right, take care

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