Question

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**.