Equation: A statement that asserts that two mathematical expressions are equal in value. If this is true for all values of the variables involved then it is called an identity, and where it is only true for some values it is called a conditional equation.
Inequality: A statement that uses the symbols > (greater than), < (less than), ≥ (greater than or equal to), ≤ ( less than or equal to) to indicate that one of the quantity is larger or smaller than another.
An inequality holds for all values of the variables involved. If a statement that uses one of the symbols above holds only for some values of the variables involved then it is called an inequation.
An inequality is comparable to an identity.
If you'd want to put it into easier kid friendly words, an inequality is a statement where two sides of the inequality are not equal. Equations on the other hand, two sides should always be equal, no mater how messed up hard one side might look to you. Trust me I've been there.
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equations have an = sign, inequalities do not
"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 system of equations can have any number of inequalities.
Inequalities are not reflexive. Inequalities are not commutative.
Equations have and can only have a = Inequalities have <, >, greater than or equal to, less than or equal to, or =