The value of x is [tex]\frac{-11}{3}[/tex].
Solution:
Given equation:
[tex]$\frac{-2}{x+4}=\frac{4}{x+3}[/tex]
To find the value of x:
[tex]$\frac{-2}{x+4}=\frac{4}{x+3}[/tex]
Do cross multiplication.
[tex]-2(x+3)=4(x+4)[/tex]
–2x – 6 = 4x + 16
Add 6 on both sides of the equation.
–2x = 4x + 22
Subtract 4x on both sides of the equation.
–6x = 22
Divide by –6 on both sides of the equation.
[tex]$x=\frac{-22}{6}[/tex]
[tex]$x=\frac{-11}{3}[/tex]
Checking:
Substitute x value in left side term.
[tex]$\frac{-2}{x+4}=\frac{-2}{\frac{-11}{3}+4 }[/tex]
[tex]$=\frac{-2}{\frac{-11+12}{3}}[/tex]
[tex]$=\frac{-2}{\frac{1}{3}}[/tex]
= – 6
Substitute x value in right side term.
[tex]$\frac{4}{x+3}=\frac{4}{\frac{-11}{3}+3 }[/tex]
[tex]$=\frac{4}{\frac{-11+9}{3}}[/tex]
[tex]$=\frac{4}{\frac{-2}{3}}[/tex]
= – 6
Hence the value of x is [tex]\frac{-11}{3}[/tex].
