Final answer:
A negative charge must move in the negative y-direction (-y) to experience a force in the positive x-direction (+x) when in a uniform magnetic field pointing in the positive z-direction (+z), according to the left-hand rule.
Step-by-step explanation:
To determine the direction a negative charge should move to experience a force in the positive x-direction (+x) while in a uniform magnetic field pointing in the positive z-direction (+z), we can use the right-hand rule for negative charges, which is a variation of the conventional right-hand rule. Typically, you would point your fingers in the direction of the velocity of a positive charge and curl them towards the direction of the magnetic field. Your thumb would then point in the direction of the magnet force on the positive charge. For a negative charge, the force is in the opposite direction to the thumb - this is known as the left-hand rule by analogy.
In this case, since the charge is negative and the force we're looking for is in the +x direction, you would point the fingers of your left hand in the direction of the magnetic field (which is along the +z-axis) and you want your thumb to point in the +x direction, indicating that the palm (opposite of thumb for a negative charge) faces the +x direction. Therefore, the negative charge must be moving in the negative y-direction (-y) to experience a force in the positive x-direction (+x). This corresponds with how the left-hand rule predicts the direction of the force on a negative charge.