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In the equation \( \sqrt[3]{5m + 2} = 3 \), the cube root is already isolated on one side. This is crucial because isolating the variable or the expression involving the variable allows us to focus directly on the terms we need to manipulate.
A variable, such as \( m \) in our problem, needs to be isolated before applying further operations to solve an equation. In some equations, you may need to rearrange terms using addition or subtraction to have the variable or expression by itself on one side. This clarity helps in accurately conducting mathematical operations in the next steps.
Remember, isolating the expression with the variable is an essential first step in both simplifying and understanding the problem you are trying to solve.

After isolating the variable or expression, the next step in solving cube root equations is often to eliminate the cube root by cubing both sides. Cubing both sides cancels out the cube root.
In our equation example, \((\sqrt[3]{5m + 2})^3 = 3^3\), cubing the left side, \( \sqrt[3]{5m + 2} \), simply gives us \( 5m + 2 \). Meanwhile, cubing 3 on the right side results in the value 27. This step is essential as it transforms the equation into a more straightforward problem without radicals.
When cubing each side, always remember that this mathematical operation works because cube and cube root are inverse functions: \( (\sqrt[3]{x})^3 = x \). This approach helps you move closer to solving for the variable.

Once the cube root is removed, the problem reduces to a basic linear equation. Solving linear equations involves simple arithmetic operations to find the value of the unknown variable.
For \( 5m + 2 = 27 \), we first subtract 2 from both sides to maintain balance, giving us \( 5m = 25 \). After that, divide each side by 5 to isolate \( m \), resulting in \( m = 5 \).
Solving linear equations generally involves two main operations:

• Addition or subtraction to remove constants from one side.
• Multiplication or division to solve for the variable.

Understanding these operations and their sequence is key in solving any linear equation successfully and confirming that the solution satisfies the original equation.