Solve the equation f(x+1)-g(x-2)=10 if f(x)=x+3 and g(x)=2x-1

To calculate the solutions of equation, we'll have to
determine the expressions of f(x+1) and g(x-2), first.

To
determine f(x+1), we'll substitute x by x+1 in the expression of
f(x).

f(x+1) = (x+1) + 3

We'll
remove the brackets:

f(x+1) = x + 4
(1)

We'll determine the expression of g(x-2) substituting x
by x-2:

g(x-2) = 2(x-2) -
1

We'll remove the
brackets:

g(x-2) = 2x - 4 -
1

We'll combine like
terms:

g(x-2) = 2x - 5
(2)

We'll substitute (1) and (2) in the equation that has
to be solved:

x+4-2x+5 =
10

We'll combine like
terms:

-x + 9 = 10

We'll
subtract 9 both sideS:

-x =
1

x =
-1

The only solution of the
equation is x = -1.