Question

solve.
\sqrt3{7x - 8} - 3 = 0

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

Explanation:

Step1: Isolate the cube root

Add 3 to both sides of the equation $\sqrt[3]{7x - 8}-3 = 0$ to get $\sqrt[3]{7x - 8}=3$.

Step2: Eliminate the cube root

Cube both sides of the equation $\sqrt[3]{7x - 8}=3$. We know that $(\sqrt[3]{a})^3=a$, so $(\sqrt[3]{7x - 8})^3 = 3^3$, which simplifies to $7x-8 = 27$.

Step3: Solve for x

Add 8 to both sides of the equation $7x - 8=27$: $7x=27 + 8=35$. Then divide both sides by 7: $x=\frac{35}{7} = 5$.

Answer:

$x = 5$