I used the test-point method, but you could also use the sign graph of factors method.
*Set 1st factor = 0 and solve
*Set 2nd factor = 0 and solve
Note that the two boundary points create three sections
on the graph: ,
,
and
.
Keep in mind that our inequality is .
Since we are looking for the quadratic expression to be GREATER
THAN 0, that means we need our sign to be POSITIVE.
From the interval ,
I choose to use -7 to test this interval:
(I could have used -10, -25, or -10000 as long as it is in the interval)
Graph:
*Visual showing all numbers
less than -6 or
greater than 1
I used the test-point method, but you could also use the sign graph of
factors method.
*Set 1st factor = 0 and solve
*Set 2nd factor = 0 and solve
Note that the two boundary points create three sections
on the graph: ,
, and
.
Keep in mind that our original problem is .
Since we are looking for the quadratic expression to be LESS
THAN OR EQUAL TO 0, that means we need our sign to be NEGATIVE
(OR 0).
From the interval ,
I choose to use 0 to test this interval:
(I could have used -10, -25, or -10000 as long as it is in the interval)
*Chose 2/5 from 2nd interval to
plug in for x
Graph:
*Visual showing all numbers between 1/3 and 1/2, inclusive
Last revised on Dec. 30, 2009 by Kim Seward.
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