please find the value of x in the figure

Answer:
Step-by-step explanation:
E is the midpoint of Ac & D is the midpoint of AB
DE = (1/2)BC {Midpoint theorem}
[tex]x +1 = \dfrac{1}{2}(4x - 6)\\\\\\ Multiply \ the \ whole \ equation \ by 2\\\\ 2*(x+1) =2*\dfrac{1}{2}*(4x - 6)[/tex]
2*x + 2*1 = 4x - 6
2x + 2 = 4x - 6
Add 6 to both sides
2x + 2 + 6 = 4x
2x + 8 = 4x
Subtract 2x from both sides
8 = 4x - 2x
2x = 8
Divide both sides by 2
x = 8/2
x = 4