Unfortunately, no, you are not even close to right. A plane parallel to the yz plane would have constant x but the distance of each point on the plane to the x axis would NOT be constant.
Take the general point (x, y, z). Its distance to the yz-plane (that is, the distance from (x,y,z) to (0,y,z)) is just x. Its distance from the x-axis is the distance from (x,y,z) to (x, 0, 0).
Find that distance and set it equal to x.