To solve a proportion using the cross-product (also known as the cross-multiplication) rule, two ratios are set equal. Those ratios must be in form.

1. Break Down the Problem

To solve a proportion using the cross-product rule, we need to identify two ratios of the form $\frac{a}{b} = \frac{c}{d}$. Our task is to set these ratios equal.

2. Relevant Concepts

The cross-product rule states that if $\frac{a}{b} = \frac{c}{d}$, then the cross-products can be calculated as follows: $a \cdot d = b \cdot c$

3. Analysis and Detail

• Step 1: Identify the two ratios. For example, if we have $\frac{2}{3} = \frac{x}{6}$, we can define $a = 2$, $b = 3$, $c=x$, and $d=6$.
• Step 2: Apply the cross-product rule. This gives: $2 \cdot 6 = 3 \cdot x$
• Step 3: Calculate the left side: $12 = 3x$
• Step 4: Solve for $x$ by dividing both sides by 3: $x = \frac{12}{3} = 4$

4. Verify and Summarize

We check our solution by substituting $x = 4$ back into the original ratio: $\frac{2}{3} \text{ is equivalent to } \frac{4}{6}.$ Both fractions simplify to $\frac{2}{3}$, confirming our solution is correct.

Final Answer

The value of $x$ is $4$.