Solve 4m^2x=m+x+1/2

$$4 m ^ { 2 } x = m + x + \frac { 1 } { 2 }$$

Solve for x

$$\left\{\begin{matrix}x=\frac{1}{2\left(2m-1\right)}\text{, }&m\neq \frac{1}{2}\\x\in \mathrm{R}\text{, }&m=-\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$4m^{2}x-x=m+\frac{1}{2}$$

Combine all terms containing x.

$$\left(4m^{2}-1\right)x=m+\frac{1}{2}$$

Divide both sides by 4m^{2}-1.

$$\frac{\left(4m^{2}-1\right)x}{4m^{2}-1}=\frac{m+\frac{1}{2}}{4m^{2}-1}$$

Dividing by 4m^{2}-1 undoes the multiplication by 4m^{2}-1.

$$x=\frac{m+\frac{1}{2}}{4m^{2}-1}$$

Divide m+\frac{1}{2} by 4m^{2}-1.

$$x=\frac{1}{2\left(2m-1\right)}$$

Solve for m

$$\left\{\begin{matrix}\\m=-\frac{1}{2}=-0.5\text{, }&\text{unconditionally}\\m=\frac{1}{2}+\frac{1}{4x}\text{, }&x\neq 0\end{matrix}\right.$$