To find the value of \( x \) such that the ratio \( \frac{x}{x+4} \) is equal to \( \frac{3}{5} \), we follow these steps:
1. Set up the given ratio as an equation:
[tex]\[
\frac{x}{x+4} = \frac{3}{5}
\][/tex]
2. Cross-multiply to eliminate the fractions. Cross-multiplication involves multiplying the numerator of each fraction by the denominator of the other fraction:
[tex]\[
x \cdot 5 = 3 \cdot (x+4)
\][/tex]
3. Distribute the constants through the parentheses on the right side:
[tex]\[
5x = 3(x + 4)
\][/tex]
[tex]\[
5x = 3x + 12
\][/tex]
4. Isolate the variable \( x \) by moving all terms involving \( x \) to one side. Subtract \( 3x \) from both sides:
[tex]\[
5x - 3x = 12
\][/tex]
[tex]\[
2x = 12
\][/tex]
5. Solve for \( x \) by dividing both sides of the equation by 2:
[tex]\[
x = \frac{12}{2}
\][/tex]
[tex]\[
x = 6
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{6} \)[/tex].
