# How do you solve #6x^2+x>1#?

##### 1 Answer

#### Explanation:

Factoring

we have

which will be equal to zero when

We not interested in when

Rather we are interested in the ranges set up by these "boundaries"

That is we are interested in the ranges:

We can test each of these ranges by picking any easily evaluated sample value of

and then seeing if that value satisfies the required inequality.

For example:

#{:(,"|","in range " x < -1/2,"in range "x in (-1/2,1/3),"in range "x > 1/3), (,"|",underline("sample: " x=-1),underline("sample: "x=0),underline("sample: "x=+1)), (6x^2+x,"|",color(white)("XXX")5,color(white)("XXX")-1,color(white)("XXX")7), (6x^2+x > 1?,"|","True","False","True") :}#