Answer: [tex]x=\frac{6}{-3y+8}[/tex]
Step-by-Step Explanation:
Let's solve for [tex]x[/tex].
[tex]\frac{x-2}{3y-5} =\frac{x}{3}[/tex]
Step 1: Multiply both sides by [tex]3y-5[/tex].
[tex]x-2=\frac{3xy-5x}{3}[/tex]
Step 2: Multiply both sides by [tex]3[/tex].
[tex]3x-6=3xy-5x[/tex]
Step 3: Add [tex]-3xy[/tex] to both sides.
[tex]3x-6+-3xy=3xy-5x+-3xy[/tex]
[tex]-3xy+3x-6=-5x[/tex]
Step 4: Add [tex]5x[/tex] to both sides.
[tex]-3xy+3x-6+5x=-5x+5x[/tex]
[tex]-3xy+8x-6=0[/tex]
Step 5: Add [tex]6[/tex] to both sides.
[tex]-3xy+8x-6+6=0+6[/tex]
[tex]-3xy+8x=6[/tex]
Step 6: Factor out variable [tex]x[/tex].
[tex]x(-3y+8)=6[/tex]
Step 7: Divide both sides by [tex]-3y+8[/tex].
[tex]\frac{x(-3y+8)}{-3y+8}=\frac{6}{y-3y+8}[/tex]
[tex]x=\frac{6}{-3y+8}[/tex]
Answer:
[tex]x=\frac{6}{-3y+8}[/tex]
