Solve f(x-4)-1=3(2x-3)

$$f ( x - 4 ) - 1 = 3 ( 2 x - 3 )$$

Solve for f

$$f=-\frac{2\left(4-3x\right)}{x-4}$$

$$x\neq 4$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by x-4.

$$fx-4f-1=3\left(2x-3\right)$$

Use the distributive property to multiply 3 by 2x-3.

$$fx-4f-1=6x-9$$

Add 1 to both sides.

$$fx-4f=6x-9+1$$

Add -9 and 1 to get -8.

$$fx-4f=6x-8$$

Combine all terms containing f.

$$\left(x-4\right)f=6x-8$$

Divide both sides by x-4.

$$\frac{\left(x-4\right)f}{x-4}=\frac{6x-8}{x-4}$$

Dividing by x-4 undoes the multiplication by x-4.

$$f=\frac{6x-8}{x-4}$$

Divide 6x-8 by x-4.

$$f=\frac{2\left(3x-4\right)}{x-4}$$

Solve for x

$$x=-\frac{4\left(2-f\right)}{f-6}$$

$$f\neq 6$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by x-4.

$$fx-4f-1=3\left(2x-3\right)$$

Use the distributive property to multiply 3 by 2x-3.

$$fx-4f-1=6x-9$$

Subtract 6x from both sides.

$$fx-4f-1-6x=-9$$

Add 4f to both sides.

$$fx-1-6x=-9+4f$$

Add 1 to both sides.

$$fx-6x=-9+4f+1$$

Add -9 and 1 to get -8.

$$fx-6x=-8+4f$$

Combine all terms containing x.

$$\left(f-6\right)x=-8+4f$$

The equation is in standard form.

$$\left(f-6\right)x=4f-8$$

Divide both sides by f-6.

$$\frac{\left(f-6\right)x}{f-6}=\frac{4f-8}{f-6}$$

Dividing by f-6 undoes the multiplication by f-6.

$$x=\frac{4f-8}{f-6}$$

Divide -8+4f by f-6.

$$x=\frac{4\left(f-2\right)}{f-6}$$