Answer:
x=-1/2
Step-by-step explanation:
[tex]\frac{5x-2}{3x+1}=9\\\\\frac{5x-2}{3x+1}*(3x+1)=9*(3x+1)\\\\5x-2=9(3x+1)\\\\5x-2=9(3x)+9(1)\\\\5x-2=27x+9\\\\5x-2-9=27x+9-9\\\\5x-11=27x\\\\5x-5x-11=27x-5x\\\\0-11=22x\\\\-11=22x\\\\-11=11(2x)\\\\-11*(\frac{1}{11})=\frac{11(2x)}{11}\\\\-1=2x\\\\x=-\frac{1}{2}[/tex]
and now we check
[tex]\frac{5(-\frac{1}{2})-2}{3(-\frac{1}{2})+1}=9\\\\\frac{-2.5-2}{-1.5+1}=9\\\\\frac{-4.5}{-0.5}=9\\\\\frac{4.5}{0.5}=9\\\\\frac{\frac{9}{2}}{\frac{1}{2}}=9\\\\\frac{9*2}{1*2}=9\\\\\frac{9}{1}=9\\\\9=9[/tex]
so the answer is -1/2
