Solve sum2x+12=3x-31

$$\sum 2 x + 12 = 3 x - 31$$

Solve for x

$$x=-\frac{43}{Σ_{2}-3}$$

$$Σ_{2}\neq 3$$

Steps for Solving Linear Equation

Subtract 3x from both sides.

$$Σ_{2}x+12-3x=-31$$

Subtract 12 from both sides.

$$Σ_{2}x-3x=-31-12$$

Subtract 12 from -31 to get -43.

$$Σ_{2}x-3x=-43$$

Combine all terms containing x.

$$\left(Σ_{2}-3\right)x=-43$$

Divide both sides by Σ_{2}-3.

$$\frac{\left(Σ_{2}-3\right)x}{Σ_{2}-3}=-\frac{43}{Σ_{2}-3}$$

Dividing by Σ_{2}-3 undoes the multiplication by Σ_{2}-3.

$$x=-\frac{43}{Σ_{2}-3}$$

Solve for Σ_2

$$Σ_{2}=3-\frac{43}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 12 from both sides.

$$Σ_{2}x=3x-31-12$$

Subtract 12 from -31 to get -43.

$$Σ_{2}x=3x-43$$

The equation is in standard form.

$$xΣ_{2}=3x-43$$

Divide both sides by x.

$$\frac{xΣ_{2}}{x}=\frac{3x-43}{x}$$

Dividing by x undoes the multiplication by x.

$$Σ_{2}=\frac{3x-43}{x}$$

Divide 3x-43 by x.

$$Σ_{2}=3-\frac{43}{x}$$