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Solving linear equations can be simple if you follow a step-by-step approach. The given exercise is a perfect example. Here's a breakdown of the steps involved:
Firstly, identify the equation you need to solve. In this case, it's \[ x - \frac{1}{5} = 4 \]. This means we need to find the value of \( x \) that makes this equation true.
Next, isolate the variable. This often means getting the variable on one side of the equation by itself. To do this, you'll usually add, subtract, multiply, or divide both sides of the equation by the same number or term.
In our example, we add \( \frac{1}{5} \) to both sides to cancel out the \( \frac{1}{5} \) on the left side.
Finally, simplify the equation. Combine like terms and simplify any fractions if necessary to solve for the variable.

Isolating the variable is a crucial part of solving equations. It means getting the variable on its own on one side of the equation. Here's how to do it:
In our equation \[ x - \frac{1}{5} = 4 \], we need to get \( x \) by itself.
We do this by performing the opposite operation. Since we have \( -\frac{1}{5} \) next to \( x \), we add \( \frac{1}{5} \) to both sides of the equation. This cancels out the fraction on the left and modifies the right side:
\[ x - \frac{1}{5} + \frac{1}{5} = 4 + \frac{1}{5} \]
This yields \[ x = \frac{21}{5} \]. By mastering the skill of isolating the variable, you simplify the process of solving equations.

Fractions in equations might seem difficult, but they're not so bad! Dealing with them often just means being careful and orderly.
When fractions appear, remember to combine them correctly. For example, in our equation \[ x - \frac{1}{5} = 4 \], we treated the fraction just like any other number.
Add \( \frac{1}{5} \) to both sides to eliminate it from the side with the variable:
\[ x - \frac{1}{5} + \frac{1}{5} = 4 + \frac{1}{5} \]
This simplifies to:
\[ 4 + \frac{1}{5} = \frac{20}{5} + \frac{1}{5} = \frac{21}{5} \]
Adding fractions means finding a common denominator. In this case, 4 becomes \( \frac{20}{5} \) so we can add it to \( \frac{1}{5} \). Practice these steps and fractions won't be intimidating!