1. Let's start by stating the problem: Solve for $x$ in the equation $7x + 25 = 11x + 5$. 2. The goal when solving equations is to group like terms together, meaning terms involving $x$ on one side and constant terms on the other side. 3. We can subtract $11x$ from both sides to move all $x$ terms to the left side: $$7x - 11x + 25 = 11x - 11x + 5$$ which simplifies to $$7x - 11x + 25 = 5$$. 4. Next, subtract $25$ from both sides to move constants to the right: $$7x - 11x + 25 - 25 = 5 - 25$$ which simplifies to $$7x - 11x = 5 - 25$$. 5. Simplify each side: $$7x - 11x = -4x$$ and $$5 - 25 = -20$$, so we have $$-4x = -20$$. 6. Finally, divide both sides by $-4$ to solve for $x$: $$x = \frac{-20}{-4} = 5$$. 7. To summarize, grouping like terms means moving all terms with $x$ to one side and constants to the other by adding or subtracting the same terms from both sides. The order in which you write them does not change the solution as long as you maintain equality. 8. For your examples, both $7x - 11x = 25 + 5$ and $-11x + 7x = 5 + 25$ are valid rearrangements as long as you consistently apply the same operations to both sides. However, the key is to keep the $x$ terms on the same side and constants on the other to solve effectively.