Answer:
[tex]x=-\frac{261}{46}[/tex]
Step-by-step explanation:
we have the expression
[tex]\frac{3x+2y-5z}{y-4z}=\frac{x}{3y}[/tex]
we have
[tex]y=6,z=-\frac{1}{2}[/tex]
To find the value of x, substitute the given values of y and z in the expression
[tex]\frac{3x+2(6)-5(-\frac{1}{2})}{6-4(-\frac{1}{2})}=\frac{x}{3(6)}[/tex]
solve for x
[tex]\frac{3x+12+\frac{5}{2}}{6+2}=\frac{x}{18}[/tex]
[tex]\frac{3x+12+\frac{5}{2}}{8}=\frac{x}{18}[/tex]
Multiplying in cross
[tex](3x+12+\frac{5}{2})18=8x[/tex]
[tex]54x+216+45=8x[/tex]
[tex]54x-8x=-216-45[/tex]
[tex]46x=-261[/tex]
[tex]x=-\frac{261}{46}[/tex]
