Question

solve.
\sqrt{5x - 4} - 1 = 3

select the correct choice below and fill in any answer boxes present in your choice.
a. x = \square (simplify your answer. use a comma to separate answers as needed.)
b. there is no solution.

Explanation:

Step1: Isolate the square root term

Add 1 to both sides of the equation.
$\sqrt{5x - 4} = 3 + 1$
$\sqrt{5x - 4} = 4$

Step2: Eliminate the square root

Square both sides of the equation.
$(\sqrt{5x - 4})^2 = 4^2$
$5x - 4 = 16$

Step3: Solve for x

Add 4 to both sides, then divide by 5.
$5x = 16 + 4$
$5x = 20$
$x = \frac{20}{5} = 4$

Step4: Verify the solution

Substitute $x=4$ back into the original equation.
$\sqrt{5(4) - 4} - 1 = \sqrt{20 - 4} - 1 = \sqrt{16} - 1 = 4 - 1 = 3$, which matches the right-hand side.

Answer:

A. $x=4$