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How do you know if a value is a solution for an inequality? How is this different from determining if a value is a solution to an equation?
When checking solutions of equations and inequalities there are no significant differences. You just take a possible solution and substitute that number into the original equation/inequality to see if it works.
The only difference is that for equations there is a specific list of one or more solutions to check. When checking an inequality there are usually an infinite number of possible solutions. For example, if you get x < 4 as a solution, any
number less than 4 (and there are an infinite number of numbers below 4) should work.
If you replace the equal sign of an equation with an inequality sign, is there ever a time when the same value will be a solution to both the equation and the inequality?
Yes, but only if it is an "or equal to" type of inequality.