Solve g*3(x-1)=2x-11

$$g \cdot 3 ( x - 1 ) = 2 x - 11$$

Solve for g

$$g=-\frac{11-2x}{3\left(x-1\right)}$$

$$x\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply g\times 3 by x-1.

$$3gx-g\times 3=2x-11$$

Multiply -1 and 3 to get -3.

$$3gx-3g=2x-11$$

Combine all terms containing g.

$$\left(3x-3\right)g=2x-11$$

Divide both sides by 3x-3.

$$\frac{\left(3x-3\right)g}{3x-3}=\frac{2x-11}{3x-3}$$

Dividing by 3x-3 undoes the multiplication by 3x-3.

$$g=\frac{2x-11}{3x-3}$$

Divide 2x-11 by 3x-3.

$$g=\frac{2x-11}{3\left(x-1\right)}$$

Solve for x

$$x=-\frac{11-3g}{3g-2}$$

$$g\neq \frac{2}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply g\times 3 by x-1.

$$3gx-g\times 3=2x-11$$

Multiply -1 and 3 to get -3.

$$3gx-3g=2x-11$$

Subtract 2x from both sides.

$$3gx-3g-2x=-11$$

Add 3g to both sides.

$$3gx-2x=-11+3g$$

Combine all terms containing x.

$$\left(3g-2\right)x=-11+3g$$

The equation is in standard form.

$$\left(3g-2\right)x=3g-11$$

Divide both sides by 3g-2.

$$\frac{\left(3g-2\right)x}{3g-2}=\frac{3g-11}{3g-2}$$

Dividing by 3g-2 undoes the multiplication by 3g-2.

$$x=\frac{3g-11}{3g-2}$$