To solve the equation \(\sqrt{5x - 7} = \sqrt{3x + 5}\), let's proceed with the following steps:
1. Square both sides of the equation to eliminate the square roots:
[tex]\[
(\sqrt{5x - 7})^2 = (\sqrt{3x + 5})^2
\][/tex]
This simplifies to:
[tex]\[
5x - 7 = 3x + 5
\][/tex]
2. Isolate the variable \(x\):
- Subtract \(3x\) from both sides to get the \(x\) terms together:
[tex]\[
5x - 3x - 7 = 3x - 3x + 5
\][/tex]
This simplifies to:
[tex]\[
2x - 7 = 5
\][/tex]
- Add 7 to both sides to isolate the term with \(x\):
[tex]\[
2x - 7 + 7 = 5 + 7
\][/tex]
This simplifies to:
[tex]\[
2x = 12
\][/tex]
- Finally, divide both sides by 2 to solve for \(x\):
[tex]\[
\frac{2x}{2} = \frac{12}{2}
\][/tex]
This simplifies to:
[tex]\[
x = 6
\][/tex]
Therefore, the solution to the equation \(\sqrt{5x - 7} = \sqrt{3x + 5}\) is:
[tex]\[
x = 6
\][/tex]
From the given options, we select:
[tex]\( x = 6 \)[/tex].
