Radical Equations Quick Check

Question

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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Answer 1

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 \( x = \frac{7}{5} \).