Solve {l}{f(2x+1)+2f(1-2x)=x-5}{text{Jikanilai}f(-1)=f(1),operatorname{dan}f^-1(-2a/3)=3}{text{makanilai}a^2-1=ldots}{text{A}16}{text{B.}15}{text{C}8}{text{Jawab:}}

$$\left. \begin{array} { l } { f ( 2 x + 1 ) + 2 f ( 1 - 2 x ) = x - 5 } \\ { \text { Jika nilai } f ( - 1 ) = f ( 1 ) , \operatorname { dan } f ^ { - 1 } ( \frac { - 2 a } { 3 } ) = 3 } \\ { \text { maka nilai } a ^ { 2 } - 1 = \ldots } \\ { \text { A } 16 } \\ { \text { B. } 15 } \\ { \text { C } 8 } \\ { \text { Jawab: } } \end{array} \right.$$

Solve for x

$$x=\frac{3f+5}{2f+1}$$

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

Steps for Solving Linear Equation

Use the distributive property to multiply f by 2x+1.

$$2fx+f+2f\left(1-2x\right)=x-5$$

Use the distributive property to multiply 2f by 1-2x.

$$2fx+f+2f-4xf=x-5$$

Combine f and 2f to get 3f.

$$2fx+3f-4xf=x-5$$

Combine 2fx and -4xf to get -2fx.

$$-2fx+3f=x-5$$

Subtract x from both sides.

$$-2fx+3f-x=-5$$

Subtract 3f from both sides.

$$-2fx-x=-5-3f$$

Combine all terms containing x.

$$\left(-2f-1\right)x=-5-3f$$

The equation is in standard form.

$$\left(-2f-1\right)x=-3f-5$$

Divide both sides by -1-2f.

$$\frac{\left(-2f-1\right)x}{-2f-1}=\frac{-3f-5}{-2f-1}$$

Dividing by -1-2f undoes the multiplication by -1-2f.

$$x=\frac{-3f-5}{-2f-1}$$

Divide -5-3f by -1-2f.

$$x=\frac{3f+5}{2f+1}$$