Question 133916: Again, i need someone to come to the aid of an old lady..Thank you so much
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 with an inequality sign, is there ever a time when the same value will be a solution to both the equation and the inequality? Write an inequality and provide a value that may or may not be a solution to the inequality.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Equations and inequalities are very much alike in one respect, the same basic tecniques are used to solve them.
There is one major difference howeverm between equations and inequalities; equations have a discrete number of solutions, depending, of course, upon the degree of the equation.
For example, equations of the first degree, otherwise known as linear equations, have only one solution, whereas, equations of the second degree, also known as quadratic equations, have two solutions.
So, in general, the number of discrete solutions to an equation is the same as the degree of the equation.
Inequalities, on the other hand, have solutions that consist of a range of values, rather than just one or two.
Here are soms simple examples of inequalities
 Subtract 4 from each side.
 Here, you can see that the solution (x) can be any number that is larger than, but not equal to 6. So to verify the solution, you would select a number that is larger than 6 and substitute it for x in the solution. Try 7, for example:
 This is a true statement, so 7 was a valid number to use for a check.
Let's look at another inequality:
 Subtract 8 from both sides.
 Divide both sides by 2.
 Now in this case, you can see that the variable, y, can be any number that is less than, or equal to, 6. So, if you were to use 6 to check your solution, it will work. Substitute y = 6.
 This is a true statement.
Now, if you were to replace the (<=) sign with an (=) sign, lets see what would happen:
 Subtract 8 from both sides.
 Divide both sides by 2.
 Here, solution consists of only one number, and that is 6.
The answer to your question about replacing the equal sign with an inequality sign and is there a value that will satisfy both; the answer is yes, but only when the inequality is <= (less than or equal to) or >= (greater than or equal to).
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