Thread: inequality/proof type thing

okay, so i need to find:
A) for which values of x is x^2 + x + 1 >= (x-1)/(2x-1)

and another similar one

for which values of x is -3x^2 +4x > 1?

Originally Posted by mistykz

okay, so i need to find:
A) for which values of x is x^2 + x + 1 >= (x-1)/(2x-1)

and another similar one

for which values of x is -3x^2 +4x > 1?

Mmmk.

A)

Get rid of the fraction on the RHS. Multiply through by 2x-1.









Can you take it from here?

(Sorry if I messed up the algebra. It's late and I did it in my head, but you get the idea I hope)

Originally Posted by mistykz

okay, so i need to find:
A) for which values of x is x^2 + x + 1 >= (x-1)/(2x-1)

and another similar one

for which values of x is -3x^2 +4x > 1?

Hello,

for confirmation only I give you the solution of the first one:



#2.

. Now factor the LHS of the inequaltiy:

. You have a product of 2 factors which is positiv. That means both factors must have the same sign. The sign + means that the value is greater than zero, the sign - ...:

. Solve each inequality:

. Collect the results of inequalities which are connected by :

Now we make the sign of each factor in a table and we use the rule of signs.



From the last row in the table we have

awesome, thanks everyone!