It’s funny how a seemingly straightforward mathematical problem can lead us down a little rabbit hole of thought, isn't it? Take the equation 2x - 1 = 11. On the surface, it’s just a basic algebra problem, something many of us encountered back in school. But as we dig a little deeper, it reveals a neat little puzzle about how we approach and solve problems.
First things first, let's tackle that initial equation: 2x - 1 = 11. The goal here is to isolate 'x', to figure out what number it represents. We can do this by using the fundamental properties of equations. Think of an equation like a balanced scale. Whatever you do to one side, you must do to the other to keep it balanced.
So, to get rid of that '-1' on the left side, we add 1 to both sides: 2x - 1 + 1 = 11 + 1. This simplifies to 2x = 12. Now, 'x' is being multiplied by 2. To get 'x' all by itself, we divide both sides by 2: (2x)/2 = 12/2. And voilà, we find that x = 6.
Now, this is where the problem gets a bit more interesting. We're not just asked to solve for 'x'; we're asked to use that value of 'x' in a new expression: 4x + 1.5x + 11. This is a common scenario in math – using the result of one calculation to solve another. It’s like finding a key and then using it to open a different door.
We know x = 6, so we substitute that into the expression: 4(6) + 1.5(6) + 11. Let's break that down:
- 4 times 6 is 24.
- 1.5 times 6 is 9.
- And then we add the 11.
So, we have 24 + 9 + 11. Adding these together, 24 + 9 gives us 33, and then 33 + 11 equals 44.
It’s a neat little process, isn't it? We start with a simple linear equation, find the value of the unknown, and then plug that value into a more complex expression. The reference materials show various ways this problem is presented, sometimes as a multiple-choice question, sometimes just asking for the calculation. Regardless of the format, the core steps remain the same: solve the equation, then substitute and calculate.
What's really valuable here isn't just the final number, 44. It's the understanding of the process. It’s about recognizing that mathematical concepts build on each other. Solving for 'x' isn't just an isolated skill; it's a tool that unlocks further calculations and problem-solving opportunities. It’s a reminder that even the most complex-looking problems often have a clear, logical path to a solution if we just take them one step at a time.
