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In solving linear equations, such as 0 = -5x, one of the first steps is to isolate the variable. This is a foundational concept pivotal to understanding algebra. The process of isolating the variable involves manipulating the equation to end up with the variable on one side and all other numbers on the opposite side. To achieve this, use inverse operations that undo the operations applied to the variable.

In our example, the variable x has a coefficient of -5. Isolating x here is straightforward because we only need to divide both sides of the equation by -5. Remember, what you do to one side, you must also do to the other to maintain the equation's balance. After the division, the equation simplifies to 0 = x, which shows that the variable is isolated on one side, and the solution is evident.

The variable coefficient is the number that is directly multiplied by the variable in an equation. In many cases, it's a fundamental step to understand the coefficient as it indicates how the variable will be manipulated to achieve isolation. In the given equation 0 = -5x, the coefficient is -5. This numerical factor affects the value of the variable x.

The inverse operation used to neutralize a coefficient is division or multiplication, depending on the operation indicated by the coefficient. Here, since the coefficient is -5 (indicating multiplication by -5), we divide by -5 to isolate x. It is important to note that dividing by a negative will affect the sign of the resulting variable value, so always pay careful attention to this detail.

After solving an equation, such as finding that x = 0 in our example, performing a substitution check is critical to ensure the solution is correct. This involves re-inserting the solution back into the original equation to confirm that it holds true (maintains equality).

For our equation 0 = -5x, we substitute x with 0, resulting in 0 = -5(0), which simplifies to 0 = 0. This true statement validates that our solution is correct. Always make it a habit to carry out this check. It not only confirms the accuracy of your solution but also reinforces understanding of how the solution fits within the original problem.