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The substitution method is a powerful tool to determine whether a given value solves an equation. You start by taking the value you want to test and substitute it into the equation in place of the variable. In this exercise, we substitute the value \(x = -2\) into the equation \[5 - 2x = -4x + 1\]. By replacing every instance of \(x\) with \(-2\), we get a new equation purely in terms of numbers. This process helps us to see if both sides of the equation remain equal after the substitution.
Step-by-step substitution ensures clarity and helps avoid errors.
Without carefully substituting and simplifying step-by-step, it’s easy to make mistakes. Therefore, it’s crucial to follow each step methodically.

After substitution, the next essential step is to simplify the expressions on both sides of the equation. Simplification involves performing operations such as addition, subtraction, multiplication, and division to reduce the expressions to their simplest form.
For our example, substituting \(x = -2\) gives us \[5 - 2(-2) = -4(-2) + 1\].
To simplify, follow these steps:

• First, solve inside the parentheses: \( -2 (-2) = 4\)
• This changes our equation to: \[5 + 4 = 8 + 1\].
• Next, perform the addition: \[5 + 4 = 9\] and \[8 + 1 = 9\].

Simplifying expressions is critical before comparing both sides, as it ensures the equation is accurately analyzed.

The final part of solving an algebraic equation using substitution is verification. Verification means confirming that both sides of the simplified equation are equal.
In our case, after substituting \(x = -2\) and simplifying, we reached \[9 = 9\]. Since both sides are equal, this verifies our chosen value of \(x = -2\) is indeed a solution to the equation \[5 - 2x = -4x + 1\].
Verification is crucial as it affirms the correctness of the solution. Without this step, there could be uncertainty regarding the accuracy of the substitution and simplification processes.