What must be done to both sides of an equation if one side is multiplied by a certain value?

• A. Subtract the same value from both sides
• B. Subtract the value from one side
• C. Add the same value to the other side
• D. Multiply the other side by the same value

Answer: (D)

When one side of an equation is multiplied by a certain value, it is essential to maintain the equality of the equation. This is achieved by performing the same operation on both sides of the equation. In this case, multiplying both sides by the same value ensures that the relationship expressed by the equation remains valid.

For instance, if you have an equation like (x = y), and you multiply one side by a value (k), you must multiply the other side by (k) as well to maintain the equality. This results in (kx = ky), which accurately reflects the same relationship as the original equation.

This principle is foundational in algebra, as it reinforces the concept that an equation can only remain equal if the same operation is applied consistently across both sides. Thus, multiplying the other side by the same value is the correct action to take in this scenario.