Solve 5x−3−−−−−−√5=2 and choose the correct value.(1 point)Responsesx=45x equals Start Fraction 4 over 5 End Fractionx=35x equals Start Fraction 3 over 5 End Fractionx=−295x equals negative Start Fraction 29 over 5 End Fractionx=7

Answer 1

To solve the equation \( \sqrt{5x - 3} = 2 \), we need to eliminate the square root by squaring both sides:

\[ 5x - 3 = 2^2 \] \[ 5x - 3 = 4 \]

Next, we add 3 to both sides:

\[ 5x = 4 + 3 \] \[ 5x = 7 \]

Now, we divide both sides by 5:

\[ x = \frac{7}{5} \]

Now we can check to see if this solution is among the provided options. The solution \( x = \frac{7}{5} \) does not match any of the exact responses given. Let's verify the solution:

1. Convert \( x = \frac{7}{5} \) to a decimal:

   • \( \frac{7}{5} = 1.4 \)

2. Substitute \( x = \frac{7}{5} \) back into the original equation:

\[ \sqrt{5 \cdot \frac{7}{5} - 3} = \sqrt{7 - 3} = \sqrt{4} = 2 \]

Thus, the solution \( x = \frac{7}{5} \) is correct.

Since this option is not in the list, it appears there might be an error in the listed responses. However, the solution to the equation is:

x = \( \frac{7}{5} \) or 1.4.