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Cross-multiplication is a simple yet powerful technique used to solve proportions, which are equations that express the equality of two ratios. In the problem \( \frac{x}{6} = \frac{18}{4} \), our goal is to find the value of \( x \) that makes this equation true. The process begins by multiplying the numerator of one fraction by the denominator of the other fraction.

For this specific equation, you will multiply \( x \) by 4, and it results in the product \( 4x \). Then, multiply 6 by 18, which results in 108. By setting these two products equal to each other, the equation now becomes \( 4x = 108 \). This cross-multiplication helps transform the proportion into a simpler equation that is easier to solve.

Remember, cross-multiplication only applies when you have one proportion set equal to another. It provides a direct path to solve for the unknown variable.

Once you have applied cross-multiplication and arrived at the equation \( 4x = 108 \), the next step is to solve for \( x \). This means we want to isolate \( x \) on one side of the equation to find its value.

In order to do this, you'll divide both sides of the equation by 4. This operation will leave \( x \) isolated on its own, so you'll have:

• Divide the left side: \( \frac{4x}{4} = x \)
• Divide the right side: \( \frac{108}{4} = 27 \)

Therefore, \( x = 27 \). This is the value that satisfies the original proportion. It's important to remember the order of operations and perform the same mathematical operation on both sides of the equation to maintain balance.

Finally, it's essential to verify that your solution is correct by checking it against the original proportion. For the problem \( \frac{x}{6} = \frac{18}{4} \), substitute the value of \( x = 27 \) back into the equation.

You'll get \( \frac{27}{6} \) on the left side, and when you simplify it, it equals 4.5. On the right side, simplify \( \frac{18}{4} \) to also get 4.5. Since both sides are equal, this confirms that \( x = 27 \) is indeed the correct solution.

Checking your solution after solving is a crucial step because it ensures that you did not make any errors during your calculations. Verifying the equality on both sides of the proportion not only boosts confidence in your result but also strengthens your understanding of solving proportions effectively.