Solve like terms in 1 minute

Hey math whizzes! Ever find yourself staring down an equation with division AND subtraction, especially when you need to compare two expressions? It used to feel like a huge headache for me, but I've picked up some tricks to simplify these problems, and I promise you can too, often in just a minute once you get the hang of it! The core of tackling these multi-operation equations, particularly for comparison, really boils down to understanding the basics we often hear about: Combine, Distribute, Divide. But how do they all play together when division and subtraction are involved? First, let's talk about the golden rule: Order of Operations (PEMDAS/BODMAS). This is your roadmap to no confusion. Always remember to handle Parentheses/Brackets first, then Exponents/Orders, followed by Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). When you're trying to combine division and subtraction in a single equation, this order is non-negotiable. You’ll always perform any division before any subtraction unless parentheses dictate otherwise. For example, in 10 - 6 / 2, you must divide 6 / 2 first to get 3, then subtract 10 - 3 to get 7. If it were (10 - 6) / 2, you'd subtract inside the parentheses first to get 4, then divide by 2 to get 2. Now, for those comparison problems. These are often about figuring out if one side of an equation is greater than, less than, or equal to the other side. Let's say you need to compare (20 / 4) - 2 with 15 - (18 / 3). My personal strategy is to simplify each side completely first. For the left side, (20 / 4) is 5, then 5 - 2 gives 3. For the right side, (18 / 3) is 6, then 15 - 6 gives 9. Now, comparing 3 and 9 is easy: 3 < 9. See? No confusion! This step-by-step approach makes it so much easier. Sometimes, you might encounter expressions where you need to distribute before you can divide or subtract effectively. For instance, if you have (2x - 6) / 2, you can actually distribute the division to each term inside the parentheses: (2x / 2) - (6 / 2), which simplifies to x - 3. This is a powerful technique for simplifying. After distribution and performing division, you might find yourself needing to combine like terms, just like in the OCR example 8y + 14y. If you had x - 3 + 5x, you'd combine x and 5x to get 6x - 3. So, my best advice for mastering these types of equations and solving them quickly? Practice! Break down each problem. Divide the problem into smaller, manageable steps. Focus on one operation at a time, following the order. And remember to combine like terms only after you've simplified as much as possible. With a little practice, you'll be tackling these in 1 minute flat, and those tricky comparison problems will become a breeze!