Answer:
[tex]\boxed {\boxed {\sf XY= 11}}[/tex]
Step-by-step explanation:
We are asked to find the value of XY.
We know that Y is the midpoint of XZ. The midpoint of a line bisects the line or divides it into 2 equal parts. The point Y divides the line XZ into 2 parts : XY and YZ. Since Y is the midpoint, XY and YZ are equal.
[tex]XY= YZ[/tex]
We know that XY is equal to 3x+2 and YZ is equal to x+8.
[tex]3x+2=x+8[/tex]
Now we can solve for x by isolating the variable. Move all the terms with variables to one side and the constants to the other side. Subtract x from both sides of the equation.
[tex](3x-x) +2 = (x-x)+8[/tex]
[tex]2x+2=8[/tex]
Subtract 2 from both sides of the equation.
[tex]2x+(2-2)= (8-2)[/tex]
[tex]2x=6[/tex]
Divide both sides of the equation by 2.
[tex]2x/2= 6/2[/tex]
[tex]x= 6/2 \\x=3[/tex]
Now we know that x is equal to 3 and we can substitute it back into 3x+2 to solve for XY.
[tex]XY= 3x+2 \\XY=3(3) +2\\XY=9+2 \\XY=11[/tex]
