Question 36

Dividing both sides of an equation by the same nonzero number always yields an equivalent equation.

Dividing both sides of an equation by the same nonzero number maintains the equality of the equation, ensuring that the relationship between both sides remains true.

A) Adding a nonzero number or algebraic expression to a given expression always yields an equivalent expression

This statement is incorrect as it does not apply to equations. While adding the same nonzero number or algebraic expression to both sides of an equation maintains equality, adding to one side alone does not yield an equivalent expression.

B) Dividing both sides of an equation by the same nonzero number always yields an equivalent equation

This statement is true because dividing both sides of an equation by the same nonzero number preserves the equality. It is a fundamental property of equations, ensuring that both sides remain equivalent.

C) Multiplying or dividing a given expression by a nonzero number or an algebraic expression always yields an equivalent expression

This statement is misleading. While multiplying or dividing both sides of an equation by the same nonzero number preserves equality, doing so to a single expression does not necessarily yield an equivalent expression without reference to an equation.

D) Adding an algebraic expression to one side of a given equation always yields an equivalent equation

This statement is incorrect. Adding an algebraic expression to only one side of an equation changes the equality unless the same expression is added to both sides. Thus, it does not yield an equivalent equation.

Conclusion

The correct answer, B, is definitively right because it adheres to the properties of equality in algebra. All other options fail as they either misinterpret the conditions for maintaining equivalence in equations or do not apply the necessary operations uniformly across both sides of an equation.