The Solution to the equation f(x) = g(x) can be found by equating both functions and evaluating value of x.
The solution will be [tex]x = 2[/tex]
Given that:
[tex]f(x) = 2x+1[/tex]
[tex]g(x) = -x+7[/tex]
To find:
Solution of the equation [tex]f(x) = g(x)[/tex]
Equating both equations and evaluating x:
[tex]f(x) = 2x + 1\\g(x) = -x + 7\\\\f(x) = g(x)\\2x + 1 = -x + 7\\\\\text{Adding x on both sides}\\2x + x + 1 = -x + x + 7\\3x + 1 = 7\\\\\text{Subtracting 1 from both sides}\\3x + 1 - 1 = 7 - 1\\3x = 6\\\\\text{Dividing both sides by 3}\\\dfrac{3x}{3} = \dfrac{6}{3}\\\\x = 2[/tex]
Thus, the solution to the given equation is [tex]x = 2[/tex].
Learn more about solutions of system of linear equations here:
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