To solve the given proportion [tex]\(\frac{2}{7} = \frac{12}{x}\)[/tex], we can use the method of cross multiplication. Cross multiplication allows us to eliminate the fractions by creating a single equation that we can solve for [tex]\(x\)[/tex].
Here are the steps:
1. Start with the given proportion:
[tex]\[
\frac{2}{7} = \frac{12}{x}
\][/tex]
2. Cross multiply to set up an equation without fractions. This involves multiplying the numerator of each fraction by the denominator of the other fraction:
[tex]\[
2 \cdot x = 7 \cdot 12
\][/tex]
3. Simplify the right side of the equation:
[tex]\[
2x = 84
\][/tex]
4. To isolate [tex]\(x\)[/tex] and solve for it, divide both sides of the equation by 2:
[tex]\[
x = \frac{84}{2}
\][/tex]
5. Perform the division:
[tex]\[
x = 42
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(42\)[/tex].
