Solve each equation. ⁵√ 2x = ⁵√ 3x+2

Key Concepts

Radical Equations

Radical equations involve variables within a radical symbol, such as square roots or cube roots. To solve these equations, one typically isolates the radical on one side and then raises both sides of the equation to the power that eliminates the radical. Understanding how to manipulate these equations is crucial for finding the values of the variable.

Properties of Exponents

Properties of exponents are rules that govern how to handle expressions involving powers. For instance, when dealing with roots, the nth root of a number can be expressed as a fractional exponent (e.g., ⁵√x = x^(1/5)). This concept is essential for rewriting radical expressions in a more manageable form, facilitating easier calculations.

Isolating Variables

Isolating variables is a fundamental algebraic technique used to solve equations. It involves rearranging the equation to get the variable of interest on one side by performing inverse operations. This concept is vital in solving equations, especially when dealing with multiple terms or radicals, as it allows for a clearer path to finding the solution.