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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.



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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