How to Solve a Quadratic Inequality with Two Variables?

[skyturnred]

Homework Statement

-1<2x$^{2}$-x<1

Homework Equations

The Attempt at a Solution

I can't seem to solve this.. I am in calculus but I get to this point at the end of a long question, and it seems so trivial that I didn't think it would be a good idea to post this in the calculus forum.

How do you solve this? I know (from wolframalpha) that the answer is -1/2<x<1 but I don't know how it got this.

 

[Mark44]

Homework Statement

-1<2x$^{2}$-x<1

Homework Equations

The Attempt at a Solution

I can't seem to solve this.. I am in calculus but I get to this point at the end of a long question, and it seems so trivial that I didn't think it would be a good idea to post this in the calculus forum.

How do you solve this? I know (from wolframalpha) that the answer is -1/2<x<1 but I don't know how it got this.

The inequality is equivalent to
0 < 2x² - x + 1 < 2,
which is the same as these two inequalities:
0 < 2x² - x + 1 AND 2x² - x + 1 < 2

Do you know how to solve these quadratic inequalities?

Graphically, the solution set to your inequality is the set of x values on the graph of y = 2x² - x for which -1 < y < 1.

 

[skyturnred]

The inequality is equivalent to
0 < 2x² - x + 1 < 2,
which is the same as these two inequalities:
0 < 2x² - x + 1 AND 2x² - x + 1 < 2

Do you know how to solve these quadratic inequalities?

Graphically, the solution set to your inequality is the set of x values on the graph of y = 2x² - x for which -1 < y < 1.

OK thanks! Splitting it up into two inequalities really makes it much easier to think about.