Which formula would be used to solve for variable x when given a proportion?

To solve for the variable x in a proportion, the appropriate method is cross-multiplication. When two ratios are set equal to each other, cross-multiplication involves multiplying the numerator of one ratio by the denominator of the other ratio. This technique helps to eliminate the fractions and produce a simple equation that can then be solved for the unknown variable.

For instance, if you have a proportion like (\frac{a}{b} = \frac{c}{d}), you would cross-multiply to get (a \cdot d = b \cdot c). This results in a straightforward multiplication equation that can then be manipulated to isolate x.

The other methods listed do not directly apply to the process of solving proportions. Direct substitution may work in certain equations but does not specifically address proportions. Graphical representation can provide a visual understanding but is not a method for solving the proportion algebraically. Algebraic expansion involves rewriting expressions but does not specifically pertain to the proportional relationships necessary to isolate the variable.