Difficulty: Medium

Average Score: 71%

The chart shows the measurements of the height of a child at 3, 6, and 9 months of age. The equation H= T+21 can be used to model the relationship between the height II, in inches, and age T, in months.

Which of the following statements is true?

Rationale

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

When an equation is divided by the same nonzero number on both sides, the equality is maintained, ensuring that the two sides remain equivalent. This principle is crucial in algebra and is a key method for solving equations.

A (Adding a nonzero number or algebraic expression to a given expression always yields an equivalent expression.) YOUR ANSWER

This statement is incorrect because adding a nonzero number or algebraic expression to one side of an equation without doing the same to the other side does not maintain the equality. Only when the same addition is applied to both sides can equivalence be achieved.

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

This statement is true. When both sides of an equation are divided by the same nonzero number, the equality remains intact, thereby producing an equivalent equation. This operation is foundational in algebraic manipulations.

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

While multiplying an expression by a nonzero number maintains equivalence, this statement lacks clarity regarding equations. It doesn't specify that both sides of an equation must be treated equally; thus, this statement can lead to misunderstanding regarding its application in equations.

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

This statement is false because adding an algebraic expression to one side of an equation without adding it to the other side alters the equation’s balance, resulting in an inequality rather than an equivalence.

Conclusion

In algebra, maintaining the balance of an equation is fundamental to achieving equivalent forms. Dividing both sides of an equation by the same nonzero number is a reliable method to keep the equation valid, which is why option B is correct. The other options fail to uphold the principles of equality in algebra when transformations are not uniformly applied.

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