Question
Solve the cube root equation 411x−15−−−−−−−√3+21=1
4
11
𝑥
−
15
3
+
21
=
1
.(1 point)
Responses
x=14011
𝑥
=
140
11
x equals Start Fraction 140 over 11 End Fraction
x=1011
𝑥
=
10
11
x equals Start Fraction 10 over 11 End Fraction
x=−911
𝑥
=
−
9
11
x equals negative Start Fraction 9 over 11 End Fraction
x=−10
4
11
𝑥
−
15
3
+
21
=
1
.(1 point)
Responses
x=14011
𝑥
=
140
11
x equals Start Fraction 140 over 11 End Fraction
x=1011
𝑥
=
10
11
x equals Start Fraction 10 over 11 End Fraction
x=−911
𝑥
=
−
9
11
x equals negative Start Fraction 9 over 11 End Fraction
x=−10
Answers
GPT-4o mini
To solve the equation \( \sqrt[3]{411x - 15} + 21 = 1 \), we first isolate the cube root term:
1. Subtract 21 from both sides:
\[
\sqrt[3]{411x - 15} = 1 - 21
\]
\[
\sqrt[3]{411x - 15} = -20
\]
2. Cube both sides to eliminate the cube root:
\[
411x - 15 = (-20)^3
\]
\[
411x - 15 = -8000
\]
3. Add 15 to both sides:
\[
411x = -8000 + 15
\]
\[
411x = -7985
\]
4. Divide both sides by 411 to solve for \( x \):
\[
x = \frac{-7985}{411}
\]
Now we can simplify \(-7985/411\). Since the numbers can be divided, we compute it:
- Divide \( 7985 \) by \( 411 \) (you can use a calculator for precision):
\[
7985 \div 411 \approx 19.4 \text{ (not an integer so we use it as is.)}
\]
Thus, the exact value remains as:
\[
x = \frac{-7985}{411}
\]
For simplification, check if \( 7985 \) and \( 411 \) share a common factor or divisibility. However, \( 7985 \) appears to be divisible by \( 5 \) and \( 11 \) but \( 411 \) is larger.
Without factorization finding brings \( 411 = 3 \times 137 \) and \( 7985 = 5 \times 79 \) without common factors.
Now, converting to an approximate fraction:
- Upon using a calculator for long division, we get to
So the answer is not included among the provided choices.
But if you want to see from provided, we have:
- Check \( x = \frac{-9}{11} \) or \( x = -10 \)
- They do not fit \( -7985/411 \)
In conclusion, we can remain with option \( \approx -19.4 \)
For the provided choices, none exactly matches our calculation.
Final \( x \) cannot be reflected from given response, which could match the \( -10 \) or non exactly resembling.
And thus direct return would require verification.
So provided responses do not yield exact math output but:
Final answer remains \( \frac{-7985}{411} \) which is \( ≈ -19.4 \). So please reconfirm inputs.
1. Subtract 21 from both sides:
\[
\sqrt[3]{411x - 15} = 1 - 21
\]
\[
\sqrt[3]{411x - 15} = -20
\]
2. Cube both sides to eliminate the cube root:
\[
411x - 15 = (-20)^3
\]
\[
411x - 15 = -8000
\]
3. Add 15 to both sides:
\[
411x = -8000 + 15
\]
\[
411x = -7985
\]
4. Divide both sides by 411 to solve for \( x \):
\[
x = \frac{-7985}{411}
\]
Now we can simplify \(-7985/411\). Since the numbers can be divided, we compute it:
- Divide \( 7985 \) by \( 411 \) (you can use a calculator for precision):
\[
7985 \div 411 \approx 19.4 \text{ (not an integer so we use it as is.)}
\]
Thus, the exact value remains as:
\[
x = \frac{-7985}{411}
\]
For simplification, check if \( 7985 \) and \( 411 \) share a common factor or divisibility. However, \( 7985 \) appears to be divisible by \( 5 \) and \( 11 \) but \( 411 \) is larger.
Without factorization finding brings \( 411 = 3 \times 137 \) and \( 7985 = 5 \times 79 \) without common factors.
Now, converting to an approximate fraction:
- Upon using a calculator for long division, we get to
So the answer is not included among the provided choices.
But if you want to see from provided, we have:
- Check \( x = \frac{-9}{11} \) or \( x = -10 \)
- They do not fit \( -7985/411 \)
In conclusion, we can remain with option \( \approx -19.4 \)
For the provided choices, none exactly matches our calculation.
Final \( x \) cannot be reflected from given response, which could match the \( -10 \) or non exactly resembling.
And thus direct return would require verification.
So provided responses do not yield exact math output but:
Final answer remains \( \frac{-7985}{411} \) which is \( ≈ -19.4 \). So please reconfirm inputs.