Question
Solve the radical equation 210x+3−−−−−−√3=6
.(1 point)
Responses
x=−310
x equals Start Fraction negative 3 over 10 End Fraction
x=125
x equals Start Fraction 12 over 5 End Fraction
x=21310
x equals Start Fraction 213 over 10 End Fraction
x=35
.(1 point)
Responses
x=−310
x equals Start Fraction negative 3 over 10 End Fraction
x=125
x equals Start Fraction 12 over 5 End Fraction
x=21310
x equals Start Fraction 213 over 10 End Fraction
x=35
Answers
GPT-4o mini
To solve the equation \( \sqrt[3]{210x + 3} = 6 \), we start by cubing both sides to eliminate the cube root:
\[
\sqrt[3]{210x + 3} = 6
\]
Cubing both sides, we get:
\[
210x + 3 = 6^3
\]
Calculating \( 6^3 \):
\[
6^3 = 216
\]
Now the equation is:
\[
210x + 3 = 216
\]
Next, we subtract 3 from both sides:
\[
210x = 216 - 3
\]
\[
210x = 213
\]
Now, we divide both sides by 210:
\[
x = \frac{213}{210}
\]
We can simplify this fraction:
\[
x = \frac{213 \div 3}{210 \div 3} = \frac{71}{70}
\]
So our final answer, which does not seem to match any options provided above, suggests that you might need to check the options again as the solution, \(\frac{71}{70}\), is not listed.
If we revisit the provided options:
1. \(x = -\frac{3}{10}\)
2. \(x = \frac{12}{5}\)
3. \(x = \frac{213}{10}\)
4. \(x = 35\)
None of these match our calculated x-value of \(\frac{71}{70}\).
If you can please double-check the equation given for any misinterpretation or if there's any alternative wording or form, we can assist further. However, based on the solution steps, none of the provided responses is correct.
\[
\sqrt[3]{210x + 3} = 6
\]
Cubing both sides, we get:
\[
210x + 3 = 6^3
\]
Calculating \( 6^3 \):
\[
6^3 = 216
\]
Now the equation is:
\[
210x + 3 = 216
\]
Next, we subtract 3 from both sides:
\[
210x = 216 - 3
\]
\[
210x = 213
\]
Now, we divide both sides by 210:
\[
x = \frac{213}{210}
\]
We can simplify this fraction:
\[
x = \frac{213 \div 3}{210 \div 3} = \frac{71}{70}
\]
So our final answer, which does not seem to match any options provided above, suggests that you might need to check the options again as the solution, \(\frac{71}{70}\), is not listed.
If we revisit the provided options:
1. \(x = -\frac{3}{10}\)
2. \(x = \frac{12}{5}\)
3. \(x = \frac{213}{10}\)
4. \(x = 35\)
None of these match our calculated x-value of \(\frac{71}{70}\).
If you can please double-check the equation given for any misinterpretation or if there's any alternative wording or form, we can assist further. However, based on the solution steps, none of the provided responses is correct.