Question

Solve each equation

Answer 1

`\large\boxed{2.\ x=-3\ \vee\ x=3}\\\boxed{5.\ x=-(4)/(11)}\\\boxed{8.\ x=18}`

Explanation:

`2.\ Domain:\ x\\eq0\\\\(1)/(x)-(x)/(9)=0\qquad\text{add}\ (x)/(9)\ \text{to both sides}\\\\(1)/(x)=(x)/(9)\qquad\text{cross multiply}\\\\(x)(x)=(1)(9)\\\\x^2=9\to x=\pm\sqrt9\\\\x=-3\ \vee\ x=3\\======================`

`5.\ Domain:x\in\mathbb{R}\\\\(3x)/(4)=(5x+1)/(3)\qquad\text{cross multiply}\\\\(3x)(3)=(4)(5x+1)\qquad\text{use the distributive property}\\\\9x=(4)(5x)+(4)(1)\\\\9x=20x+4\qquad\text{subtract 20x from both sides}\\\\-11x=4\qquad\text{divide both sides by (-11)}\\\\x=-(4)/(11)\\======================`

`8.\ Domain:\ x+3\\eq0\to x\\eq-3\\\\(2x-1)/(x+3)=(5)/(3)\qquad\text{cross multiply}\\\\3(2x-1)=5(x+3)\qquad\text{use the distributive property}\\\\(3)(2x)+(3)(-1)=(5)(x)+(5)(3)\\\\6x-3=5x+15\qquad\text{add 3 to both sides}\\\\6x=5x+18\qquad\text{subtract 5x from both sides}\\\\x=18\\======================`