Answer
$x = 4$
Work Step by Step
Rewrite the exponent as a radical:
$2\sqrt[3] {2x} + 1 = 5$
Isolate the radical:
$2\sqrt[3]{2x}=5-1\\
2\sqrt[3] {2x} = 4\\
\sqrt[3]{2x}=2 \quad \quad \text{(divide both sides by $2$)}$
Cube both sides of the equation to eliminate the radical:
$2x = 8$
$x = 4$
To check if we have an extraneous solution, we substitute the solution into the original equation to see if the two sides equal one another.
$2\sqrt[3] {2(4)} + 1 = 5$
Simplify the radicand:
$2\sqrt[3] {8} + 1 = 5$
Take the cube root:
$2(2) + 1 = 5$
Multiply first:
$4 + 1 = 5$
Combine like terms:
$5 = 5$
Both sides are equal; therefore, this solution is valid.
