1. The problem states that a point $P(10,6)$ is dilated from the origin using the rule $(x,y) \to (0.3x, 0.3y)$. 2. The dilation rule means each coordinate of the point is multiplied by $0.3$. 3. To find the x-coordinate of the image point $P'$, apply the rule to the x-coordinate of $P$: $$x' = 0.3 \times 10$$ 4. Calculate the product: $$x' = 3$$ 5. Therefore, the x-coordinate of $P'$ after dilation is $3$.