Question 84442: Solve
-4t>2
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! You can work the solution of these following the same rules that you would for an equation,
with one big exception. In solving an inequality, if you need to multiply or divide
both sides by a minus quantity, do the multiplication or division AND REVERSE the direction of
the inequality sign.
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Given problem:
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-4t > +2
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Solve for +t by dividing both sides of the inequality by -4, the multiplier of t.
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Dividing both sides by -4 results in:
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t > 2/(-4)
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But don't forget the rule. You divided both sides by a minus quantity so you need to
reverse the direction of the inequality sign. The answer becomes:
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t < 2/(-4)
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and you can clean up the right side of the equation by recognizing that 2/(-4) is the
same as -1/2. So the answer is:
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t < -1/2
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This means that t can be any value on the number line as long as it is to the left of
the value -1/2.
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Let's do a simple check just to check the possibility that this answer is correct.
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Let's say t = -1. That certainly is to the left of -1/2 on the number line. Substitute
that value for t into the given problem.
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-4t > +2
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-4*(-1) > +2
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+4 > +2
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That works. So our answer seems correct. Next, just as another check let's assume that
t = 0. That value is NOT to the left of -1/2 so it should NOT work. Plug 0 in for t
in the original problem and you get:
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-4*0 > +2
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0 > +2
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That value for t does NOT work. This helps further to build our confidence that t must
be less than -1/2.
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Hope this helps you to understand a little more about solving inequalities. Remember
that you can pretty much go about solving them by following the same processes and steps
that you would use to solve an equation, with that one exception of reversing the
inequality sign if you multiply or divide both sides by a minus quantity.
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