what is the solution to the equation $sqrt{5x - 7}=sqrt{3x + 5}$?\n$x = 1$\n$x = 6$\n$x = 12$\n$x = 24$

Explanation:

Step1: Square both sides

Since $\sqrt{5x - 7}=\sqrt{3x + 5}$, squaring both sides gives $5x-7 = 3x+5$.

Step2: Move like - terms

Subtract $3x$ from both sides: $5x-3x-7=3x - 3x+5$, which simplifies to $2x-7 = 5$.

Step3: Isolate the variable term

Add 7 to both sides: $2x-7 + 7=5 + 7$, getting $2x=12$.

Step4: Solve for x

Divide both sides by 2: $\frac{2x}{2}=\frac{12}{2}$, so $x = 6$.

Answer:

$x = 6$