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Inequalities

Inequalities are manipulated algebraically the same way as equations with one exception:
 
Note: Multiplying or dividing both sides of an inequality by a negative number reverses the inequality. That is, if x > y and c < 0, then cx < cy.
 
Example

For which values of x is 4x + 3 > 6x – 8 ?

As with equations, our goal is to isolate x on one side:

 

Subtracting 6x from both sides yields –2x + 3 > –8
Subtracting 3 from both sides yields –2x > –11
Dividing both sides by –2 and reversing the inequality yields x < 11/2

 





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