To solve the proportion $\frac{7}{10} = \frac{14}{x}$, we can use the technique of cross-multiplication.

In essence, solving a proportion means finding the value of an unknown variable that makes both ratios equivalent. In this case, we are given the proportion $\frac{7}{10} = \frac{14}{x}$. The method of cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction and setting these two products equal to each other.

Let’s break it down step by step:

1. Cross-multiply the fractions:

   $$7 \cdot x = 10 \cdot 14$$

   This simplifies to:

   $$7x = 140$$

2. Isolate the variable by solving for $x$. To do this, divide both sides of the equation by $7$:

   $$\frac{7x}{7} = \frac{140}{7}$$

   This simplifies to:

   $$x = 20$$

Thus, the value of $x$ that makes the proportion $\frac{7}{10}$ equal to $\frac{14}{x}$ is $20$. This approach guarantees that the two ratios remain balanced and equivalent throughout the calculation.