Question 419740: Solve
(x+5)(x-4)(x+4)>0
a the solution set is
b the solution is all real numbers
c there is no solution
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! dividing by the other 2 factors reduces this equation to:
x+5 > 0
x+4 > 0
x-4 >0
this makes the solution set any of:
x > -5
x > -4
x > 4
this implies that x > 4 is one of the solutions.
x > -4 and x > -4 should also be one of the solutions, but you have to be careful with the signs.
you have 3 factors.
if all of the factors are positive, then the answer is > 0.
if all of the factors are negative, then the answer is < 0
if any of the factors is equal to 0, then the answer is = 0.
if one of the factors is negative and one is positive, then the answer is > 0.
if one of the factors is positive and two of the factors are negative, then the answer is < 0.
the easiest way to see what is happening is to graph this equation.
this might be considered cheating, but it's the quickest way to show you what is happening.
the graph of this equation looks like this:
from this graph, you can see that it looks like the equation is > 0 when:
x > 4
x > -5
x < -4
anywhere else, the equation is negative.
to test this out, you need to solve for individual values of x to see what happens to the equation.
i'll use excel to create a table for you so you can see what the results would be easy enough.
without this table, you would have to test at:
x = -5, x = -4, x = 4
x = some value less than -5.
x = some value between -5 and -4
x = some value between x = -4 and x = 4
x = some value greater than 4
you'll see these values from the table.
x f(x) f(x) > 0
-6 -20
-5.5 -7.125
-5 0
-4.5 2.125 ***** IS > 0
-4 0
-3.5 -5.625
-3 -14
-2.5 -24.375
-2 -36
-1.5 -48.125
-1 -60
-0.5 -70.875
0 -80
0.5 -86.625
1 -90
1.5 -89.375
2 -84
2.5 -73.125
3 -56
3.5 -31.875
4 0
4.5 40.375 ***** IS > 0
from this table, you can see that:
when x is greater than -5 and less than -4, the value of the equation is positive.
when x is greater than 4, the value of the equation is positive.
that's your answer.
the answer would be that the value of the equation is > 0 when:
-5 < x < -4 or x > 4
when x = -5 or x = -4 or x = 4, the value of the equation is equal to 0 which is not > 0.
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