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The multiplication principle can also be used to divide both sides of an equation. Choose the correct statement below of how this can be done. A. Multiply by -x on both sides. B. Multiply by the reciprocal of the coefficient of x on both sides. C. Multiply by the multiplicative identity on both sides. D. Multiply by x on both sides.

Ask by King Phillips. in the United States
Feb 26,2025

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The correct statement is B: Multiply by the reciprocal of the coefficient of x on both sides.

Solución

The correct statement is B. When you "divide" both sides by the coefficient of x, you are in fact multiplying both sides by its reciprocal. This is because division is equivalent to multiplication by the reciprocal.

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Bonus Knowledge

To effectively isolate a variable in an equation, it's common to use the reciprocal. Thus, the correct statement is B. Multiply by the reciprocal of the coefficient of x on both sides. This method allows you to keep the equation balanced while removing the coefficient attached to x. Understanding this principle dates back to ancient civilizations like the Babylonians, who were among the first to systematically solve linear equations. They might not have called it the "multiplication principle," but they certainly understood the importance of maintaining balance on both sides of an equation, paving the way for the algebra we use today!

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