\( \sqrt{5 x-4}=4 \) he solution set is

To solve the equation \( \sqrt{5x - 4} = 4 \), start by squaring both sides to eliminate the square root: \( 5x - 4 = 16 \). Next, add 4 to both sides: \( 5x = 20 \). Now, divide by 5 to find \( x \): \( x = 4 \). So, the solution set is \( \{ 4 \} \). Remember to check your solution by substituting back into the original equation: \( \sqrt{5(4) - 4} = \sqrt{20 - 4} = \sqrt{16} = 4 \), confirming that \( x = 4 \) is indeed correct! Now, let us delve into the importance of checking solutions and common mistakes when handling square roots. Sometimes, it's easy to forget that squaring both sides can introduce extraneous solutions! Always plug your answers back into the original equation to verify they work, as we just did here. Also, keep an eye out for potentially leading to negative or undefined solutions—though in this case, we were safe!