Answer:
[tex]x=-\frac{2}{3}[/tex]
Explanation:
Let:
[tex]f(x)=-3x+4\\\\And\\\\g(x)=2[/tex]
We need to know for which value of [tex]x[/tex] the function [tex]f(x)[/tex] is equal to [tex]g(x)[/tex]:
[tex]f(x)=g(x)[/tex]
Therefore, we need to solve for the previous equation for [tex]x[/tex]:
Replacing the values of [tex]f(x)[/tex] and [tex]g(x)[/tex]:
[tex]-3x+4=2[/tex]
Subtract 4 from both sides:
[tex]-3x+4-4=2-4\\\\-3x=-2[/tex]
Multiply both sides by -1
[tex]-3x(-1)=-2(-1)\\\\3x=2[/tex]
Divide both sides by 3:
[tex]\frac{3x}{3} =\frac{2}{3} \\\\x=\frac{2}{3}[/tex]
Therefore the value of [tex]x[/tex] for which [tex]f(x)=g(x)[/tex] is [tex]x=\frac{2}{3}[/tex].
Verify the result:
[tex]-3(\frac{2}{3} )+4=2\\\\-2+4=2\\\\2=2[/tex]
