Solve {c}{f(x+2)=x+f(x)}{f(1)=-5Rightarrowf(11)=?}

$$\left. \begin{array} { c } { f ( x + 2 ) = x + f ( x ) } \\ { f ( 1 ) = - 5 \Rightarrow f ( 11 ) = ? } \end{array} \right.$$

Solve for f, x

$$x=-10$$

$$f=-5$$

Solution Steps

Consider the second equation. Divide both sides by 1.

$$f=-5$$

Consider the first equation. Insert the known values of variables into the equation.

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

Use the distributive property to multiply -5 by x+2.

$$-5x-10=x-5x$$

Combine x and -5x to get -4x.

$$-5x-10=-4x$$

Add 4x to both sides.

$$-5x-10+4x=0$$

Combine -5x and 4x to get -x.

$$-x-10=0$$

Add 10 to both sides. Anything plus zero gives itself.

$$-x=10$$

Divide both sides by -1.

$$x=-10$$

The system is now solved.

$$f=-5 x=-10$$