EXPLANATION
We can affirm by the triangle midsegment theorem that the segment DF is half of the segment BC, therefore:
[tex]DF=\frac{1}{2}BC[/tex]
Plugging in the terms into the expression:
[tex](4x-3)=\frac{1}{2}(6(x+1))[/tex]
Applying the distributive property and removing the parentheses:
[tex]4x-3=3x+3[/tex]
Subtracting -3x to both sides:
[tex]4x-3x-3=3[/tex]
Subtracting terms:
[tex]x-3=3[/tex]
Adding +3 to both sides:
[tex]x=3+3[/tex]
Adding numbers:
[tex]x=6[/tex]
In conclusion, the value of x is 6
