Solve 2mx+x+2=10

$$2 m x + x + 2 = 10$$

Solve for m

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

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$2mx+2=10-x$$

Subtract 2 from both sides.

$$2mx=10-x-2$$

Subtract 2 from 10 to get 8.

$$2mx=8-x$$

The equation is in standard form.

$$2xm=8-x$$

Divide both sides by 2x.

$$\frac{2xm}{2x}=\frac{8-x}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$m=\frac{8-x}{2x}$$

Divide 8-x by 2x.

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

Solve for x

$$x=\frac{8}{2m+1}$$

$$m\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Subtract 2 from both sides.

$$2mx+x=10-2$$

Subtract 2 from 10 to get 8.

$$2mx+x=8$$

Combine all terms containing x.

$$\left(2m+1\right)x=8$$

Divide both sides by 2m+1.

$$\frac{\left(2m+1\right)x}{2m+1}=\frac{8}{2m+1}$$

Dividing by 2m+1 undoes the multiplication by 2m+1.

$$x=\frac{8}{2m+1}$$