SOLUTION: 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? If you replace the equal sign of an equa

Question 222429: 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? If you replace the equal sign of an equation and put an inequality sign in its place, is there ever a time when the same value will be a solution to both the equation and inequality?
Found 2 solutions by rapaljer, solver91311:
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
The solution to an EQUATION is actually the endpoint of an interval that would be the solution for a corresponding INEQUALITY.

If you are asking if you can solve an inequality by solving an EQUATION and then just replace the equal sign with the inequality sign, the answer is NO! Definitely NO! The rules for solving inequalities are similar to the rules for solving equations, but definitely NOT the same. For more explanation on this, please see my own website. Do a "Bing" search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of the search list.

On my Homepage near the top, look for the link "Basic, Intermediate and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in Chapter 1 for Section 1.11 Inequalities. In this section, you will find my own non-traditional explanations, that my own students all said were a LOT easier to understand than traditional textbooks. See also the corresponding "MATH IN LIVING COLOR" pages in which problems are solved IN COLOR!

If I misunderstood your question, please send me an Email, and I'll be glad to try again.

R^2

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Replace the variable in the inequality with the value in question. If the result is a true statement, then the value is an element of the solution set of the inequality, otherwise not.

If you replace an inequality sign with an equals sign, there is one possible situation where a value will satisfy both the equation and the inequality. That is the situation where the inequality sign is inclusive of equals, i.e. or . In this case, any element of the solution set of the equation is an element of the solution set of the inequality.

John

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