What Are the Surface Charge Densities on a Conducting Slab in an Electric Field?

[heartofaragorn]

Homework Statement

An infinite sheet of charge, oriented perpendicular to the x-axis, passes through x = 0. It has area density = -3 micro C/m^2. A thick, infinite conducting slab, also oriented perpendicular to the x-axis, occupies the region between x=a and x=b where a = 4 cm and b=5 cm. The conducting slab has a net charge per unit area = 5 microC/m^2. Calulate the surface charge densities on the left hand and right had faces of the conducting slab. You may also find it useful to note the relationship between them.

Homework Equations

E = density / permittivity of free space (epsilon o)
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The Attempt at a Solution

According to my physics book, since the inside of the conductor has an electric field of zero, one can assume that the charge on the surfaces are negative and positive. I reasoned that the negative charge would like closer to the y-axis whereas the positive charge would lie on the other side. I tried using the formula above, but I'm guessing it is the wrong formula since I cannot get the correct answer this way. I also tried answers such as -3 micro C and +8 micro C to balance out the total charge of 5 micro C. Where am I going wrong?

 

[heartofaragorn]

It would help if I attached the picture!