in-3-38-solve-each-equation-for-the-variable-check-and-write-the-solution-set-1-sqrt3x74

Question

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

Nick Johnson · Accepted Answer

one minus the cube root of X plus seven is equal to four. So first, let&#x27;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&#x27;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&#x27;s under the cube root under the radical, which it&#x27;s just experts whips Whoops, which is just equal to X plus seven. Okay. And that&#x27;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

Martha Richards · Answer

So we&#x27;re asked to solve this equation for X, check it as well as provide the solutions that So when I have the radical ice later that can just square both sides and I get X on the left and seven square, it is a 49. So we&#x27;re gonna check this in the original equation squared of 49 is seven. So seven is equal to seven, so this checks out. So our solution set for these equation here is for X equal to 49.

Nick Johnson · Answer

here We have immigration. The square root of X plus four minus the square root of X minus one is equal to one. So well, if we were to Hmm. Let&#x27;s see. How about if we add, um, a square root of X minus one to both sides, So that would then give us the square root of X plus four within the equal to well, one plus the square root of X minus one. Why do we do this? But now we go ahead and square both sides. Square in the left side is just going to give us X plus four, right? The squarely of plus four square is just equal to X plus four. So but the right side we have what? One plus the square root of X minus one. So we square the right side we get while we get one plus the square root of X minus one times, right. One plus the square root of X minus one times itself. But the needs to square it Well, this was gonna equals one times. One is one. Then we get one time squid of X minus one stashed a squirt of X minus one plus right, Um, plus another one times the square X minus one that&#x27;s gonna give us while plus two times the square root of X minus one on Ben while X minus one times X minus one just gives us X minus one so that we get while plus, um plus X minus one. So plus X minus one. Okay, so squaring the left side again, the squid of X plus four squared Just could just x plus four. So we get X Plus four is gonna be equal to again squaring This gives us this year&#x27;s We get one plus two times the square root of X minus one, uh, plus X minus one. Okay, well, the exes are gonna cancel out right track action. Both sides and the exes are gone. Um, And then, well, we can go ahead and we can add one to both sides. Um, well, actually, not really. Because you have a one minus one. So that&#x27;s gonna have to cancel. It becomes zero. Okay, so let me get well, just a four is equal to two times the square root of X minus one, right. That&#x27;s what this is gonna basically simplify down too. And then we can go ahead and divide through by two to get for over two or just two is equal to the square root of X minus one. And now we can go ahead and square both sides to eliminate this square root, so squaring both sides now gives us while two square is four is equal to just X minus one. So adding one the both sides gives us that X right is equal to five. So we have that X is equal to fight, right? Just adding one to both sides. You have exercise five. Now go ahead and check the solution in our original equation. Here is this true or the square root of five plus four is just the square root of nine and then we have minus, while the square root of five minus one that&#x27;s the square root of four that should be equal toe won with a score of nine is three, and a squirt of four is to just have three minus two, which indeed is equal to one writes that simplifies down to one. Is it with the one of hat is true that checks out and therefore our solution here. X equals five is a balance solution in our solution set is the set containing just the number of five. All right, take care.

Martha Richards · Answer

sore ass to solve this equation, check it and then provide the solution side. So we&#x27;ll start here. We have the radical isolated so I can square both sides and then I get a five. Plus a un left and seven squared is 49. So if I subtract five from both sides, I get the A is equal to a 44. So then plugging that back into the original equation I get here 44 plus five is the square root of 49 and then the square root of 49 is seven. So this does indeed check out in the solution set for this equation. Here, the square root by plus a sequel. The seven. It&#x27;s seven. Oh is sorry, 44.

Martha Richards · Answer

you were asked to solve this equation, check for it and then provide the solutions that so when the radical is isolated, we can just square both sides. So I get one plus X on the left is equal to nine, cause three squared is nine. And then I subtract one on both sides, and I end up here with X equal to eight. So now let&#x27;s check this in the original equation. So I replaced acts with eight. And here, when I have eight plus one, that&#x27;s the square root of nine and the spirit of nine is three. So this does check out. So our solutions that for the equation above here is for X equal to eight.

Nick Johnson · Answer

having equation here. One plus the square root of X is equal to three. So on the left side of the equation, I have two terms, right? I have one in the square Durex. So I have an ex term and have a constant. Let&#x27;s go ahead and move. All are constants toe one side of the equation by just subtracting one from both sides. Track one from both sides. One minus 10 I just get zero plus bread of expert justice. Square root of acts is equal to three minus one squared of access equal to two and then the south for X because I have the square root of X Aiken Square, both sides to undo the square root is the square root of X squared is equal to X, and then we square both sides so excessively could the two square or two times two, which is equal to four so X secretive form, meaning that our solution set contains just the number of four. There&#x27;s our solutions said All right,

Problem

In $3-38,$ solve each equation for the variable, …

Problem 33 Medium Difficulty

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

Answer

$\{-34\}$

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$\{-34\}$

Algebra 2 and Trigonometry

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Ann Xavier Gantert

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