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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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.

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