Question
Radical Equations Quick Check
1 of 51 of 5 Items
Question
Solve 5x−3−−−−−√5=2
and choose the correct value.(1 point)
Responses
x=7
x equals 7
x=45
x equals Start Fraction 4 over 5 End Fraction
x=35
x equals Start Fraction 3 over 5 End Fraction
x=−295
x equals negative Start Fraction 29 over 5 End Fraction
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Answers
GPT-4o mini
To solve the equation \( \sqrt{5x - 3} = 2 \), we can start by squaring both sides to eliminate the square root.
\[
\sqrt{5x - 3} = 2
\]
Squaring both sides:
\[
5x - 3 = 4
\]
Now, add 3 to both sides to isolate the term involving \(x\):
\[
5x = 7
\]
Next, divide both sides by 5 to solve for \(x\):
\[
x = \frac{7}{5}
\]
Now, we'll check if this value is among the options given:
Responses:
1. \( x = 7 \)
2. \( x = \frac{4}{5} \)
3. \( x = \frac{3}{5} \)
4. \( x = -\frac{29}{5} \)
None of those options match our solution of \( x = \frac{7}{5} \), which means there might have been a misunderstanding in the given options or a miscalculation in evaluating the options.
If \( x + 1 = 2 \), then:
- Rearranging gives \( x = 1 \).
Please double-check the original equation and options for any discrepancies. Based on solving the equation provided, the result is \( x = \frac{7}{5} \).
\[
\sqrt{5x - 3} = 2
\]
Squaring both sides:
\[
5x - 3 = 4
\]
Now, add 3 to both sides to isolate the term involving \(x\):
\[
5x = 7
\]
Next, divide both sides by 5 to solve for \(x\):
\[
x = \frac{7}{5}
\]
Now, we'll check if this value is among the options given:
Responses:
1. \( x = 7 \)
2. \( x = \frac{4}{5} \)
3. \( x = \frac{3}{5} \)
4. \( x = -\frac{29}{5} \)
None of those options match our solution of \( x = \frac{7}{5} \), which means there might have been a misunderstanding in the given options or a miscalculation in evaluating the options.
If \( x + 1 = 2 \), then:
- Rearranging gives \( x = 1 \).
Please double-check the original equation and options for any discrepancies. Based on solving the equation provided, the result is \( x = \frac{7}{5} \).