Question

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

Answer 1

Answer:

$\large\boxed{x=-\dfrac{69}{2}\to x=-34\dfrac{1}{2}\to x=-34.5}$

Step-by-step explanation:

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