Which method should be used to solve an equation for the unknown variable?

Which method should be used to solve an equation for the unknown variable?

• A. Changing one side only
• B. Isolating variables by performing the same operation on both sides
• C. Adding random numbers
• D. Multiplying both sides by zero

Answer: (B)

To solve an equation for the unknown variable, isolating the variable by performing the same operation on both sides is the appropriate method. This approach relies on the principle of equality, which states that if two expressions are equal, applying the same operation to both sides maintains that equality. For example, if you have an equation like \(x + 3 = 7\), you can isolate \(x\) by subtracting 3 from both sides. This results in \(x = 7 - 3\), simplifying to \(x = 4\). The operations performed on both sides (in this case, subtraction) are crucial because they ensure that the integrity of the equation remains intact, thereby providing the correct solution for the unknown. In contrast, changing only one side of the equation disregards the balance and results in an incorrect relationship. Adding random numbers does not follow a systematic approach and can lead to confusion or incorrect solutions. Multiplying both sides by zero leads to a loss of information, as any number multiplied by zero results in zero, making it impossible to isolate the variable or derive a meaningful solution. Thus, isolating the variable correctly by applying the same operation to both sides remains the reliable method for solving equations.

To solve an equation for the unknown variable, isolating the variable by performing the same operation on both sides is the appropriate method. This approach relies on the principle of equality, which states that if two expressions are equal, applying the same operation to both sides maintains that equality.

For example, if you have an equation like (x + 3 = 7), you can isolate (x) by subtracting 3 from both sides. This results in (x = 7 - 3), simplifying to (x = 4). The operations performed on both sides (in this case, subtraction) are crucial because they ensure that the integrity of the equation remains intact, thereby providing the correct solution for the unknown.

In contrast, changing only one side of the equation disregards the balance and results in an incorrect relationship. Adding random numbers does not follow a systematic approach and can lead to confusion or incorrect solutions. Multiplying both sides by zero leads to a loss of information, as any number multiplied by zero results in zero, making it impossible to isolate the variable or derive a meaningful solution. Thus, isolating the variable correctly by applying the same operation to both sides remains the reliable method for solving equations.