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When solving linear equations, the first goal is usually to isolate the variable term. This means that you want the variable you're solving for, such as \( x \), to be on its own on one side of the equation. In the example \( \frac{x}{5} - 2 = 9 \), isolating the variable requires eliminating the constant terms from the side containing the variable. To do this, identify any constants being subtracted or added, and perform the opposite operation to both sides. Here, subtracting 2 from both sides would remove \(-2\) next to the variable, bringing us to \( \frac{x}{5} = 11 \). Always perform the same operation to both sides of the equation to maintain its balance. Once isolated, the equation is simpler and often easier to solve.

After you find a solution, checking it is a crucial step to ensure accuracy. To verify your result, substitute your solution back into the original equation. This step confirms that your calculated value satisfies the original equation, free from any arithmetic mistakes. For instance, after finding \( x = 55 \), substitute it back: \( \frac{55}{5} - 2 = 9 \). Simplify: \( 11 - 2 \) equals \( 9 \). When both sides of the equation are equal, it confirms that the solution is correct.It's easy to make small errors while solving equations, so always get in the habit of checking your work by substituting the solution back into the original equation's context.

Dealing with fractions in equations can seem tricky at first but is quite manageable with practice. To eliminate a fraction, identify its denominator and multiply both sides of the equation by this number. This process removes the fraction, which simplifies solving for the unknown variable.Take \( \frac{x}{5} = 11 \) as an example. Here, the fraction \( \frac{x}{5} \) has a denominator of 5. To clear the fraction, multiply the entire equation by 5, giving you \( x = 55 \). Once you clear the fraction, the path to the solution is straightforward.Using this approach helps simplify equations that include fractions, making them easier to solve and understand. It ensures you handle equations reliably, minimizing mistakes in calculations.