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Decimals can sometimes make equations look more complicated than they are. By clearing decimals, we can simplify the equation and make it easier to solve. This involves converting all decimal numbers into whole numbers. We do this by multiplying each term in the equation by a power of ten that will eliminate the decimals.

For example, in the equation \(0.04x - 1.9 = 0.1\), we multiply every term by 100. This removes the decimals because 100 is equivalent to moving the decimal two places to the right:

\(100 \times 0.04x - 100 \times 1.9 = 100 \times 0.1\)

The equation then becomes:

\(4x - 190 = 10\)

Now you have an equation without decimals, and it’s easier to work with integers for further steps.

Isolating the variable is crucial for solving any equation. This means rearranging the equation so that the variable (like \(x\)) is on one side of the equation, and everything else is on the other side. When the equation is \(4x - 190 = 10\), we want \(4x\) alone on one side.

We do this by performing the same operation on both sides of the equation. To isolate \(4x\), we add 190 to both sides:

\(4x - 190 + 190 = 10 + 190\)

Simplifying this, we get:

\(4x = 200\)

Now, the term with the variable \(4x\) is isolated.

After isolating the variable, we solve for it by performing operations to get the variable by itself. In our example, after isolating \(4x\), we have:

\(4x = 200\)

To find \(x\), we divide both sides of the equation by 4, since the inverse operation of multiplication is division:

\(\frac{4x}{4} = \frac{200}{4}\)

This simplifies to:

\(x = 50\)

Now we have the value of the variable. Whenever you isolate the variable and solve for it, always make sure to perform the same operations on both sides of the equation to maintain balance.