Let's tackle this algebraic puzzle together, shall we? You've asked about solving 2(4x - 1) = 18. It might look a bit daunting at first glance, but honestly, it's like peeling back layers of an onion – each step reveals something clearer.
Think of it this way: the 2 outside the parentheses is like a multiplier, eager to distribute its value. So, the very first thing we want to do is get rid of that 2 by dividing both sides of the equation by it. This is a fundamental rule in algebra: whatever you do to one side, you must do to the other to keep things balanced.
So, 2(4x - 1) = 18 becomes (4x - 1) = 18 / 2. And 18 / 2? That's a neat 9. Now our equation looks a lot friendlier: 4x - 1 = 9.
Next up, we want to isolate the term with x in it. That -1 is hanging around, and we can politely ask it to move to the other side. When a number crosses the equals sign, its sign flips. So, -1 becomes +1 on the right side.
Our equation now reads: 4x = 9 + 1. And 9 + 1 is simply 10. So, we're left with 4x = 10.
We're almost there! The 4 is currently multiplying x. To get x all by itself, we do the opposite: we divide. Again, we divide both sides by 4.
This gives us x = 10 / 4.
Now, 10/4 can be simplified. Both numbers are divisible by 2. So, 10 / 4 simplifies to 5 / 2. If you prefer decimals, that's 2.5.
And there you have it! The solution to 2(4x - 1) = 18 is x = 5/2 or x = 2.5. It’s really about taking it one step at a time, using those basic algebraic principles, and not getting flustered by the initial appearance of the problem. It’s a bit like solving a riddle – once you know the trick, it’s quite satisfying!
