91Ó°ÊÓ

The fundamental step to solving any linear equation is to isolate the variable. In our case, the variable is x. Imagine the scales of a balance being in equilibrium; our goal is to have x alone on one side. To achieve this, we perform operations on both sides that will simplify the equation while maintaining the balance. Here, dividing both sides of the equation by \(\frac{9}{10}\) is the key move.

It's like unwrapping a gift; we remove layers (in this case, the fraction \(\frac{9}{10}\)) to reveal what's inside (the value of x). Conceptually, when you divide both sides by \(\frac{9}{10}\), you're actually multiplying by its reciprocal, which is \(\frac{10}{9}\), to get x by itself. Understanding the 'why' behind each step builds a robust foundation in algebraic problem solving.

Once we've isolated the variable, the next step is equation simplification. You might think of this as decluttering a room to clearly see what's in it. In our exercise, simplifying means performing the division \(0.18 \text{ divided by } \frac{9}{10}\) which results in the value of 2 for x.

Here's a mini guide to simplify fractions:

• Divide the numerator (the top number) by the denominator (the bottom number).
• If the divisor is a fraction, multiply by its reciprocal.
• Simplify your answer, if needed, to obtain a final value.

Understanding simplification is not just about getting the right answer, it's about seeing the most direct path to it.

Verifying the solution is the last but not least important step. Think of it as double-checking the address before sending out an important letter. You want to make sure it's right! Plugging the obtained value of x back into the original equation gives us tangible proof that our solution is correct.

To verify, substitute x with 2 in the original equation \(\frac{9}{10} x=0.18\) to see if the sides are equal. If they are, it's like the lock clicks shut with the right key — you've solved the equation correctly! This step ensures that any potential mistakes made in the process are caught before they can cause problems down the road. It's not just a formality, it's a critical part of the problem-solving process. Always verify your solution to solidify your understanding and your result.