Question

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

Answer 1

$Domain:\\\\3+2x\neq0\to x\neq-1.5\\\\\dfrac{6x-4}{3+2x}=\dfrac{5}{6}\qquad\text{cross multiply}\\\\6(6x-4)=5(3+2x)\qquad\text{use distributive property}\\\\(6)(6x)+(6)(-4)=(5)(3)+(5)(2x)\\\\36x-24=15+10x\qquad\text{add 24 to both sides}\\\\36x=39+10x\qquad\text{subtract 10x from both sides}\\\\26x=39\qquad\text{divide both sides by 26}\\\\x=\dfrac{39}{26}\\\\x=\dfrac{39:13}{26:13}\\\\\boxed{x=\dfrac{3}{2}}\in D$