# Inequalities The non-strict inequalities \(\geq\) and \(\leq\) are created as infix operators with the respective syntax >=, <= Maxima allows single inequalities, such as \(x-1>y\), and also support for inequalities connected by logical operators, e.g. \( x>1 \mbox{ and } x<=5\). You can test if two inequalities are the same using the algebraic equivalence test, see the comments on this below. Chained inequalities, for example \(1\leq x \leq2\mbox{,}\) are not permitted. They must be joined by logical connectives, e.g. "\(x>1\) and \(x<7\)". As `and` and `or` are converted to `nounand` and `nounor` in student answers, you may need to use these forms in the teacher's answer as well. For more information, see [Propositional Logic](../Topics/Propositional_Logic.md). From version 3.6, support for inequalities in Maxima (particularly single variable real inequalities) was substantially improved. # Functions to support inequalities * `ineqprepare(ex)` This function ensures an inequality is written in the form `ex>0` or `ex>=0` where `ex` is always simplified. This is designed for use with the algebraic equivalence answer test in mind. * `ineqorder(ex)` This function takes an expression, applies `ineqprepare()`, and then orders the parts. For example, ineqorder(x>1 and x<5); returns 5-x > 0 and x-1 > 0 It also removes duplicate inequalities. Operating at this syntactic level will enable a relatively strict form of equivalence to be established, simply manipulating the form of the inequalities. It will respect commutativity and associativity and `and` and `or`, and will also apply `not` to chains of inequalities. If the algebraic equivalence test detects inequalities, or systems of inequalities, then this function is automatically applied. * `make_less_ineq(ex)` Reverses the order of any inequalities so that we have `A