Question

Solve: 2/3x - 3/4 = 5 + 5/6x

Answer 1

`\large\boxed{x=-(69)/(2)\to x=-34(1)/(2)\to x=-34.5}`

Explanation:

`(2)/(3)x-(3)/(4)=5+(5)/(6)x\qquad\text{multiply both sides by LCD = 12}\\\\12\!\!\!\!\!\diagup^4\cdot(2)/(3\!\!\!\!\diagup_1)x-12\!\!\!\!\!\diagup^3\cdot(3)/(4\!\!\!\diagup_1)=(12)(5)+12\!\!\!\!\!\diagup^2\cdot(5)/(6\!\!\!\diagup_1)x\\\\(4)(2x)-(3)(3)=60+(2)(5x)\\\\8x-9=60+10x\qquad\text{add 9 to both sides}\\\\8x-9+9=60+9+10x\\\\8x=69+10x\qquad\text{subtract}\ 10x\ \text{from both sides}\\\\8x-10x=69+10x-10x\\\\-2x=69\qquad\text{divide both sides by (-2)}\\\\x=-(69)/(2)`