Linear Inequalities: solve -2/(3 - x) >= 0

-2/[3-x]>=0
-2>0 impossible no solution
if you plot -2/[3-x] =2/[x-3]
y=2/[x-3] x=0 y=-2/3 x=+/-oo y=0-
function never crosses the x axis
Arthur
 
Re: Linear Inequalities

anas said:
-2/(3-x)>=0

Remember that the quotient of two NEGATIVE numbers is positive. The numerator of your fraction is negative; if the denominator is also negative, the quotient will be greater than 0.

So, we want all values of x for which

3 - x < 0

is true.

Add x to both sides of the inequality:

3 < x

or, if you'd prefer,
x > 3

Now, let's check by picking a value of x which is greater than 3, say 5. Substitute 5 for x in the original inequality:

-2 / (3 - 5) > 0

-2 / (-2) > 0

1 > 0 <--------True

The solution for this inequality, then, is all x for which x > 3.
 
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