Answer:
x=0 and x=6
Step-by-step explanation:
First, we need to set these two functions equal to each other and then we need to solve for x.
[tex]|x-2|+1=\frac{1}{3} x+3\\\\|x-2|=\frac{1}{3}x+2[/tex]
To get rid of the absolute values, we have to add both a + and a - to the other side. This will split the equation into two different equations. Lets solve for the + side first.
[tex]x-2=\frac{1}{3}x+2\\\\x=\frac{1}{3}x+4\\\\\frac{2}{3}x=4\\\\x=\frac{12}{2} =6\\\\x=6[/tex]
And now for the - side.
[tex]x-2=-\frac{1}{3}x-2\\\\x=-\frac{1}{3}x\\\\x=0[/tex]
