Solve the inequality in terms of intervals. 2x^2 + x

Question

Solve the inequality in terms of intervals.  2x^2 + x <= 1

phi · Answer

this one is tricker.  you have to move the 1 to the left side, and factor the quadratic

anonymous · Answer

|dw:1377977958266:dw|

anonymous · Answer

OH, so I need the quadratic formula for this one?

phi · Answer

true, but that is not how to factor it.

phi · Answer

I think 
2 x^2 + x -1 ≤ 0 
factors nicely
(2x   ) (x     ) ≤ 0

it looks like   2x - 1  and x+1

phi · Answer

once you get A * B ≤ 0 you have to test two cases A*B is negative (less than 0) if either 1) A < 0 and *at the same time* B > 0 (minus times a plus is minus) 2) A> 0 and at the same time B <0 same idea

phi · Answer

** in this case use ≤  or ≥  rather than < or > in the above cases

phi · Answer

in other words

2 x^2 + x -1 ≤ 0 
is the same as
(2x -1)(x+1) ≤ 0

this means the stuff on the left side is either 0 or a negative number.
you need to find when the left side is negative.  It will be negative when the two terms have opposite signs.

anonymous · Answer

Alright, so I follow now with the idea that 2x^2 +x -1 is factorable and that x = 1/2 and -1, and using the test interval method I found |dw:1377978522870:dw| How do I know what the answer is from this?  Is it the center section or the outside sections?