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To solve any linear equation, one of the key steps is to isolate the variable. This means you want to get the variable, often represented as \(x\), by itself on one side of the equation. This process simplifies finding the solution to the equation as you then clearly see the value of the variable.

For example, consider the equation \( -\frac{1}{10}=x \). In this scenario, the variable \(x\) is already isolated and is on the right side of the equality sign. This tells us directly that \(x = -\frac{1}{10}\).

In more complex equations, you may need to perform various algebraic operations to isolate the variable. These steps could include:

• Adding or subtracting terms on both sides
• Multiplying or dividing both sides by a number

Goal: Achieve a form where\( x \) is equal to some term or number.

The next important concept in solving linear equations is simplifying the equations. Simplification involves making the equation as simple as possible so that it's easy to solve.

Simplification can include:

• Combining like terms
• Reducing fractions
• Removing parentheses by applying the distributive property \((a(b+c) = ab + ac)\)

For the given exercise, \( -\frac{1}{10}=x \) is already in its simplest form. However, in more complex equations, these steps can make solving much easier.

Always simplify as much as possible before making any further steps.

Once you've isolated the variable and simplified the equation, what's left is to state the solution. This is straightforward if the previous steps were followed correctly.

In our example, the solution is given directly as \( x = -\frac{1}{10} \).

In general, the solution to a linear equation is the value of the variable that makes the equation true. To verify the solution:

• Substitute the value back into the original equation
• Ensure that both sides of the equation are equal

This verification step ensures that your isolation and simplification were performed correctly.