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Algebra - Linear Inequalities

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1. How do solving linear inequalities differ from solving linear equations?

2. What is the difference between identity, conditional, and inconsistent equations? Support your answer with an example of each.

3. What is the necessary condition for the following fraction to be valid? What value(s) of "x" that cannot be used in this fraction?
4-x/x

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The expert examines the linear inequalities. Neat and step-by-step solutions are provided.

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(1) The solution set of a system of linear equations may consist of just one unique solution or infinitely many solutions. In these cases, we say that the system is consistent. However, in some cases the system may not have a solution at all and we say the system is inconsistent.
Consider a system of linear equations that is consistent. The solution(s) consist of ordered pairs of the form (x, y). Every equation of the system holds only for these ordered pairs of x and y, and for no other.
(There are several methods of solving a system of linear equations: Addition, Substitution, and Cramer's Rule, Matrix method to name a few. The 2-variable system can be solved ...

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