Question

Which of the following is not allowed in a given equation?

• A. Adding the same number to both sides of the equation.
• B. Subtracting the same number from both sides of the equation.
• C. Multiplying both sides of the equation by the same non-zero number.
• D. Dividing both sides of the equation by the same number.

Answer 1

The correct option is D

Dividing both sides of the equation by the same number.

The explanation for the correct option:

Option (D): Dividing both sides of the equation by the same number.

Once we divide both sides of an equation by the same non-zero integer, the two sides stay equal, according to the division property of equality. Which is, if $a,b,$ and $c$ are real integers such that $a=b$ and $c\ne 0$ respectively, then $ac=ac$.
Hence, divisors of any number by zero are not permitted since the set division of a number by zero is not defined. When given an equation dividing both sides of the equation by the same integer is not permitted.

The explanation for incorrect options:

Option (A): Adding the same number to both sides of the equation.

Adding the same number to both sides of an equation does not change its solution set.

Option (B): Subtracting the same number from both sides of the equation.

Subtracting the same number to both sides of an equation does not change its solution set.

Option (C): Multiplying both sides of the equation by the same non-zero number.

Multiply both sides of a linear equation by a non-zero number, then the roots of the linear equation will remain the same.

Hence, for the division property of equality “Option A, Option B, and Option C” all options are incorrect.

Hence, the correct choice is “Option D”.