A proportion is generally multiplicative relationship between two measures of a quantity. An equation is a mathematical statement that relates two quantities. The quantities may contain a number of expressions, with each expression comprising a number of numerical constants, variables and functions.
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equations have an = sign, inequalities do not
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"What is the difference between inequalities and equations" is a question, not a statement. A question cannot be true or false. It can be pointless, or badly phrased or misguided but that is a different matter.
A calculator can be used to proportions to answer a equation. This is easier to solve when having variables on both sides.
radical equations have sq roots, cube roots etc. Quadratic equations have x2.