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By "inequations" I assume you mean "inequalities" because I can't think of anything else other than equations where the equation sign is crossed, and I don't think you mean that.
Most algebraic operations work the same in equations and inequalities; one thing to be wary with is multiplying or dividing both sides of an inequality by a negative number. Take the inequality 3 < 4. If you multiply both sides by -1, you get -3 < -4, which is incorrect; so, when you multiply or divide both sides of an inequality, be sure to invert the inequality sign.
Also, when the sign of an algebraic expression is ambiguous, I sometimes use the square of the expression, as the square of an algebraic expression not involving complex numbers will be positive; I do this to be a bit "surer" of the sign. However, this may introduce more problems, of which extraneous solutions are only the tip of the iceberg.
Sorry for the rather unnecessarily verbose answer.
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What does shading on a graph signify?
If this is related to coordinate geometry then the shading refers to the areas on the graph that satisfy the given inequations i.e if y>=2x+3 and y>= -2x+3 then the areas above both lines would be shaded.
This 19th century french mathmatician did very innovative work with inequations and quadratic forms?
Joseph Adhémar.Paul Émile Appell.François Arago.Louis François Antoine Arbogast.Jean-Robert Argand.Léon-François-Antoine Aurifeuille.Léon Autonne.
What are the properties in solving equations and inequations?
You can add, subtract, multiply, or divide both sides of the equation or inequality by the same number. Don't multiply or divide by zero. In the case of an inequality, if you multiply or divide by a negative number, the sign of the inequality must be reversed. E.g., if you multiply both sides by -2, a "less-than" sign should be replaced by a "greater-than" sign.
