Answer:
x = 6
Step-by-step explanation:
Given:
[tex]\displaystyle \large{x:(x+4)=3:5}[/tex]
The equation can be rewritten as:
[tex]\displaystyle \large{\dfrac{x}{x+4}=\dfrac{3}{5}}[/tex]
To find:
First, we have to get rid of the denominator by finding the LCM which this equation’s LCM is 5(x+4). Therefore, multiply both sides by LCM:
[tex]\displaystyle \large{\dfrac{x}{x+4}\cdot 5(x+4) = \dfrac{3}{5}\cdot 5(x+4)}\\\displaystyle \large{5x=3(x+4)}[/tex]
Then distribute 3 in x+4, for easier in solving the equation:
[tex]\displaystyle \large{5x=3x+12}[/tex]
Subtract both sides by 3x:
[tex]\displaystyle \large{5x-3x=3x+12-3x}\\\displaystyle \large{2x=12}[/tex]
Divide both sides by 2:
[tex]\displaystyle \large{\dfrac{2x}{2}=\dfrac{12}{2}}\\\displaystyle \large{x=6}[/tex]
Therefore, the value of x is 6.
