1. State the problem. Problem: Solve $194+2p=284$. 2. Formula and rules. For a linear equation of the form $ap+b=c$ isolate $p$ by first subtracting $b$ then dividing by $a$. The solution formula is $p=\frac{c-b}{a}$. 3. Step-by-step solution. Start with the given equation. $$194+2p=284$$ Subtract 194 from both sides to isolate the term with $p$. $$2p=284-194$$ Compute the subtraction on the right-hand side. $$2p=90$$ Divide both sides by 2 to solve for $p$. $$p=\frac{90}{2}$$ Show the intermediate cancellation by factoring 90 as $2\cdot 45$ and canceling the common factor 2. $$p=\frac{\cancel{2}\cdot 45}{\cancel{2}}$$ Complete the simplification to obtain the final value. $$p=45$$ 4. Final answer. Therefore the solution is $p=45$.