Question

solve.
\sqrt3{2x - 4} - 1 = 2

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. x = \square
(type an integer or a simplified fraction. use a comma to separate answers as needed.)
b. there is no real solution.

Explanation:

Step1: Isolate the cube root

Add 1 to both sides of the equation $\sqrt[3]{2x - 4}-1 = 2$ to get $\sqrt[3]{2x - 4}=2 + 1$.
Simplifying the right side, we have $\sqrt[3]{2x - 4}=3$.

Step2: Eliminate the cube root

Cube both sides of the equation $\sqrt[3]{2x - 4}=3$.
Using the property $(a^m)^n=a^{mn}$, we get $(\sqrt[3]{2x - 4})^3=3^3$.
Which simplifies to $2x-4 = 27$.

Step3: Solve for x

Add 4 to both sides of the equation $2x-4 = 27$: $2x=27 + 4$.
Simplifying the right side gives $2x=31$.
Divide both sides by 2: $x=\frac{31}{2}$.

Answer:

A. $x = \frac{31}{2}$