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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?
o 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?
o Write an inequality and provide a value that may or may not be a solution to the inequality. Consider responding to a classmate by determining whether or not the solution provided is a solution to the inequality. If the value he or she provides is a solution, provide a value that is not a solution. If the value is not a solution, provide a value that is a solution.
2 answers
a.
To solve 3x>3, proceed to solve 3x=3 to get x=1.
Examine the inequality, if x=1+something, would the inequality be satisfied? If so, as in the case of the example, then you conclude that the solution is x>1.
The above method is true for linear relations. For non-linear relations, such as x²+4x+4>0, the method will not work.
b.
If the inequality is given as ≤ or ≥, then the solution with the equality sign will satisfy both the equation and the inequality.
c.
Make an example, and post your results if you would like a check.
To solve 3x>3, proceed to solve 3x=3 to get x=1.
Examine the inequality, if x=1+something, would the inequality be satisfied? If so, as in the case of the example, then you conclude that the solution is x>1.
The above method is true for linear relations. For non-linear relations, such as x²+4x+4>0, the method will not work.
b.
If the inequality is given as ≤ or ≥, then the solution with the equality sign will satisfy both the equation and the inequality.
c.
Make an example, and post your results if you would like a check.