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When dealing with fractions, it's important to understand how to multiply them. In the exercise given, \( \frac{1}{6} x = 30 \), we see a fraction (\frac{1}{6}) multiplied by a variable (x). To get rid of the fraction, we need to multiply both sides of the equation by the fraction's reciprocal.

The reciprocal of \( \frac{1}{6} \) is 6. By multiplying both sides of the equation by 6, we effectively cancel out the fraction. Here's how:

\[ 6 \times \frac{1}{6} x = 6 \times 30 \] Multiplying by 6 on both sides simplifies the equation and brings us closer to isolating the variable.

Remember, multiplying by the reciprocal is a powerful tool for solving equations involving fractions. It allows you to convert the equation into a simpler form, making it easier to work with.

The goal in solving linear equations is to find the value of the variable. To do this, we need to isolate the variable on one side of the equation. In our exercise, after we multiplied both sides by 6: \[ 6 \times \frac{1}{6} x = 6 \times 30 \] The equation simplifies to: \[ x = 180 \]

Isolating the variable means removing everything around it so that it stands alone. In this case, multiplying by 6 removed the \( \frac{1}{6} \) from the left side, leaving us with x by itself.

Always perform the same operation on both sides of the equation to keep it balanced. Whether you add, subtract, multiply, or divide, doing the same thing to both sides will keep the equation true.

Simplifying is all about making the equation as straightforward as possible. After isolating the variable and performing operations, you often end up with a simpler form that clearly shows the solution. In the example, once we multiplied both sides of \( \frac{1}{6} x = 30 \) by 6, it simplified to: \[ x = 180 \]

Simplifying involves:

• Combining like terms
• Reducing fractions
• Clearing parentheses

The less complex the equation, the easier it is to see the solution. Always check your simplified equation to ensure it's accurate. Here, our simplified result shows clearly that x equals 180, solving the original problem.