Question

$\frac{2}{3} -4x+\frac{7}{2} =-9x+\frac{5}{6}$

Answer 1

Answer:

$\large\boxed{x=-\dfrac{2}{3}}$

Step-by-step explanation:

$\dfrac{2}{3}-4x+\dfrac{7}{2}=-9x+\dfrac{5}{6}\qquad\text{multiply both sides by LCD = 6}\\\\6\!\!\!\!\diagup^2\cdot\dfrac{2}{3\!\!\!\!\diagup_1}-(6)(4x)+6\!\!\!\!\diagup^3\cdot\dfrac{7}{2\!\!\!\!\diagup_1}=(6)(-9x)+6\!\!\!\!\diagup^1\cdot\dfrac{5}{6\!\!\!\!\diagup_1}\\\\(2)(2)-24x+(3)(7)=-54x+(1)(5)\\\\4-24x+21=-54x+5\qquad\text{combine like terms}\\\\(4+21)-24x=-54x+5\\\\25-24x=-54x+5\qquad\text{subtract 25 from both sides}\\\\25-25-24x=-54x+5-25$

$-24x=-54x-20\qquad\text{add}\ 54x\ \text{to both sides}\\\\-24x+54x=-54x+54x-20\\\\30x=-20\qquad\text{divide both sides by 30}\\\\\dfrac{30x}{30}=\dfrac{-20}{30}\\\\x=-\dfrac{2}{3}$