To find the value of \( x \) in the proportion \(\frac{x}{20} = \frac{12}{5}\):
1. Set up the proportion:
[tex]\[
\frac{x}{20} = \frac{12}{5}
\][/tex]
2. Cross-multiply to create an equation without fractions:
[tex]\[
x \cdot 5 = 20 \cdot 12
\][/tex]
3. Perform the multiplication on both sides:
[tex]\[
5x = 240
\][/tex]
4. Solve for \( x \) by dividing both sides of the equation by 5:
[tex]\[
x = \frac{240}{5}
\][/tex]
5. Simplify the right-hand side:
[tex]\[
x = 48
\][/tex]
Thus, the value of \( x \) is \( 48 \).
To check the solution, substitute \( x = 48 \) back into the original proportion to verify:
[tex]\[
\frac{48}{20} = \frac{12}{5}
\][/tex]
Simplify the left-hand side:
[tex]\[
\frac{48}{20} = \frac{24}{10} = \frac{12}{5}
\][/tex]
Since both sides of the equation are equal, the solution \( x = 48 \) is correct.
The solution set is [tex]\( \{48\} \)[/tex].
