Multiplying by zero on both sides results in an indeterminate form, division by zero is undefined in mathematics, and inequalities have different properties compared to equalities.
Multiplying by 0 on both sides: When both sides of an inequality are multiplied by zero, it results in a condition where 0 is equal to 0 times x. This condition is satisfied by any real number, leading to an indeterminate form where it's not possible to determine the value of x.
Division by zero: Dividing both sides of an inequality by zero is not possible. Division by zero is considered undefined in mathematics due to the differing reasons behind it. For example, 1/0 and 0/0 have different implications and do not yield meaningful results.
Properties of inequalities: Inequalities do not always follow the same properties as equalities. While adding, subtracting, multiplying, or dividing by the same number on both sides of an equality maintains its validity, the same operations on inequalities may not preserve the relationships between the numbers as expected.
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