Final answer:
The reason for each step in solving the equation 4x - 1 = -2(x + 1) is to systematically isolate the variable x and find its value, ultimately determining that x equals -1/6. Checking the math confirms the solution is correct.
Step-by-step explanation:
The solution to the algebraic equation 4x - 1 = -2(x + 1) involves a series of steps that systematically simplify and solve for the variable x. To begin with, we need to expand the right hand side of the equation which gives us 4x - 1 = -2x - 2. Next, we collect like terms by adding 2x to both sides resulting in 6x - 1 = -2. Following this, we add 1 to both sides to isolate the term with the variable, yielding 6x = -1. Finally, we divide both sides by 6 to solve for the unknown variable x, resulting in x = -1/6.
Check the math is an essential step after solving the equation to ensure the solution satisfies the original equation. By substituting x back into the original equation, if both sides equate, the solution is verified.