Manipulating equation for Young's Modulus and Hooke's Law

[JC2000]

Homework Statement

If a metal wire of length L, area of cross-section A and Young's modulus Y, behaves as a spring of spring constant k. Find the value of k.

Relevant Equations

Hooke's Law $F= -kx$ and Young's modulus, defined as $Y = \frac {F*L}{x*A}$

Equating the two equations gives me $k = -\frac {YA}{L}$ but the correct answer of the same magnitude but opposite sign.

I think the nub of my misunderstanding is quite elementary (who would have guessed!) : When is it $F=kx$ and when is it $F=-kx$? If I understand correctly, F is the restoring force or the 'stress' and x is the direction of displacement by the force which F opposes(?), thus with the origin at equilibrium (before any forces act), x and F would have opposing signs always?

What have I misunderstood here?
Thank you!

 

[jtbell]

The minus sign in Hooke’s Law indicates that the force F and displacement x are in opposite directions. In this problem you’re not interested in the directions, only in the magnitudes, so you can omit the minus sign.