Question

solve the equation.
\sqrt4{x - 7} = 3
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}. (simplify your answer. use a comma to separate answers as needed.)
b. there is no solution.

Explanation:

Step1: Eliminate the fourth root

To solve the equation \(\sqrt[4]{x - 7}=3\), we raise both sides to the power of 4 to eliminate the fourth root.
\((\sqrt[4]{x - 7})^4 = 3^4\)

Step2: Simplify both sides

Simplifying the left side, the fourth root and the fourth power cancel out, giving \(x - 7\). On the right side, \(3^4 = 81\). So we have the equation:
\(x - 7 = 81\)

Step3: Solve for \(x\)

Add 7 to both sides of the equation to isolate \(x\).
\(x = 81 + 7\)
\(x = 88\)

Answer:

A. The solution set is \(\{88\}\)