Question

Solve for x: 3x-a/x+2a=2a/3 __a ≠ 4.5

Answer 1

`\large\boxed{x=(4a^2+3a)/(9-2a)}`

Explanation:

`(3x-a)/(x+2a)=(2a)/(3)\qquad\text{cross multiply}\\\\(3)(3x-a)=(2a)(x+2a)\qquad\text{use the distributive property}\\\\(3)(3x)+(3)(-a)=(2a)(x)+(2a)(2a)\\\\9x-3a=2ax+4a^2\qquad\text{add}\ 3a\ \text{to both sides}\\\\9x=2ax+4a^2+3a\qquad\text{subtract}\ 2ax\ \text{from both sides}\\\\9x-2ax=4a^2+3a\qquad\text{distributive}\\\\(9-2a)x=4a^2+3a\qquad\text{divide both sides by}\ (9-2a)\\eq0\\\\x=(4a^2+3a)/(9-2a)`