To find the value of [tex]\( x \)[/tex] that makes the proportion [tex]\( \frac{3}{x} = \frac{15}{40} \)[/tex] true, follow these steps:
1. Express the Equation:
[tex]\[
\frac{3}{x} = \frac{15}{40}
\][/tex]
2. Cross-Multiply:
Cross-multiplication involves multiplying the numerator on one side by the denominator on the other side:
[tex]\[
3 \cdot 40 = 15 \cdot x
\][/tex]
3. Simplify the Equation:
Simplify the multiplication on each side:
[tex]\[
120 = 15x
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], divide both sides of the equation by 15:
[tex]\[
x = \frac{120}{15}
\][/tex]
5. Perform the Division:
Calculate the division:
[tex]\[
x = 8
\][/tex]
So, the value of [tex]\( x \)[/tex] that makes the given proportion true is [tex]\( \boxed{8} \)[/tex].
