What must be verified to ensure that an equation holds true?

• A. Only the original equation must be remembered
• B. Calculated values must be substituted into the equation
• C. One side must always be greater than the other
• D. The total must equal zero for all equations

Answer: (B)

To ensure that an equation holds true, it is essential to substitute calculated values back into the equation. This process involves taking the results derived from solving the equation and replacing the variables in the original equation with these values. If both sides of the equation equal each other after this substitution, then the equation is verified and holds true.

This method provides a concrete way to confirm accuracy and validate that the calculations performed during problem-solving were correct. It also allows for the identification of any errors in calculations or in the logical progression used to derive the values.

In contrast, simply remembering the original equation is insufficient for verification because it does not confirm that the specific calculated values are appropriate. The notion that one side of the equation must always be greater than the other is not true for valid equations; they may be equal or either side may be greater depending on the situation. The idea that the total must equal zero is conditional and generally pertains only to specific types of equations, such as those used in balancing expressions rather than as a blanket rule for all equations.