Solve afrac{sqrt{x^2}}{3}=2x-2

$$a \frac { \sqrt { x ^ { 2 } } } { 3 } = 2 x - 2$$

Solve for a

$$a=-\frac{6\left(1-x\right)}{|x|}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$a\sqrt{x^{2}}=6x-6$$

The equation is in standard form.

$$\sqrt{x^{2}}a=6x-6$$

Divide both sides by \sqrt{x^{2}}.

$$\frac{\sqrt{x^{2}}a}{\sqrt{x^{2}}}=\frac{6x-6}{\sqrt{x^{2}}}$$

Dividing by \sqrt{x^{2}} undoes the multiplication by \sqrt{x^{2}}.

$$a=\frac{6x-6}{\sqrt{x^{2}}}$$

Divide -6+6x by \sqrt{x^{2}}.

$$a=\frac{6\left(x-1\right)}{|x|}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{6}{a-6}\text{, }&a<6\\x=\frac{6}{a+6}\text{, }&a<-6\end{matrix}\right.$$