Solve f(x+2)-f(x-1)=26/3f(x)

$$f ( x + 2 ) - f ( x - 1 ) = \frac { 26 } { 3 } f ( x )$$

Solve for f (complex solution)

$$\left\{\begin{matrix}\\f=0\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&x=\frac{9}{26}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by x+2.

$$fx+2f-f\left(x-1\right)=\frac{26}{3}fx$$

Use the distributive property to multiply f by x-1.

$$fx+2f-\left(fx-f\right)=\frac{26}{3}fx$$

To find the opposite of fx-f, find the opposite of each term.

$$fx+2f-fx+f=\frac{26}{3}fx$$

Combine fx and -fx to get 0.

$$2f+f=\frac{26}{3}fx$$

Combine 2f and f to get 3f.

$$3f=\frac{26}{3}fx$$

Subtract \frac{26}{3}fx from both sides.

$$3f-\frac{26}{3}fx=0$$

Combine all terms containing f.

$$\left(3-\frac{26}{3}x\right)f=0$$

The equation is in standard form.

$$\left(-\frac{26x}{3}+3\right)f=0$$

Divide 0 by 3-\frac{26}{3}x.

$$f=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{9}{26}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by x+2.

$$fx+2f-f\left(x-1\right)=\frac{26}{3}fx$$

Use the distributive property to multiply f by x-1.

$$fx+2f-\left(fx-f\right)=\frac{26}{3}fx$$

To find the opposite of fx-f, find the opposite of each term.

$$fx+2f-fx+f=\frac{26}{3}fx$$

Combine fx and -fx to get 0.

$$2f+f=\frac{26}{3}fx$$

Combine 2f and f to get 3f.

$$3f=\frac{26}{3}fx$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{26}{3}fx=3f$$

The equation is in standard form.

$$\frac{26f}{3}x=3f$$

Divide both sides by \frac{26}{3}f.

$$\frac{3\times \frac{26f}{3}x}{26f}=\frac{3\times 3f}{26f}$$

Dividing by \frac{26}{3}f undoes the multiplication by \frac{26}{3}f.

$$x=\frac{3\times 3f}{26f}$$

Divide 3f by \frac{26}{3}f.

$$x=\frac{9}{26}$$

Solve for f

$$\left\{\begin{matrix}\\f=0\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=\frac{9}{26}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by x+2.

$$fx+2f-f\left(x-1\right)=\frac{26}{3}fx$$

Use the distributive property to multiply f by x-1.

$$fx+2f-\left(fx-f\right)=\frac{26}{3}fx$$

To find the opposite of fx-f, find the opposite of each term.

$$fx+2f-fx+f=\frac{26}{3}fx$$

Combine fx and -fx to get 0.

$$2f+f=\frac{26}{3}fx$$

Combine 2f and f to get 3f.

$$3f=\frac{26}{3}fx$$

Subtract \frac{26}{3}fx from both sides.

$$3f-\frac{26}{3}fx=0$$

Combine all terms containing f.

$$\left(3-\frac{26}{3}x\right)f=0$$

The equation is in standard form.

$$\left(-\frac{26x}{3}+3\right)f=0$$

Divide 0 by 3-\frac{26}{3}x.

$$f=0$$

Solve for x

$$\left\{\begin{matrix}\\x=\frac{9}{26}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by x+2.

$$fx+2f-f\left(x-1\right)=\frac{26}{3}fx$$

Use the distributive property to multiply f by x-1.

$$fx+2f-\left(fx-f\right)=\frac{26}{3}fx$$

To find the opposite of fx-f, find the opposite of each term.

$$fx+2f-fx+f=\frac{26}{3}fx$$

Combine fx and -fx to get 0.

$$2f+f=\frac{26}{3}fx$$

Combine 2f and f to get 3f.

$$3f=\frac{26}{3}fx$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{26}{3}fx=3f$$

The equation is in standard form.

$$\frac{26f}{3}x=3f$$

Divide both sides by \frac{26}{3}f.

$$\frac{3\times \frac{26f}{3}x}{26f}=\frac{3\times 3f}{26f}$$

Dividing by \frac{26}{3}f undoes the multiplication by \frac{26}{3}f.

$$x=\frac{3\times 3f}{26f}$$

Divide 3f by \frac{26}{3}f.

$$x=\frac{9}{26}$$