Answer:
x = 4
Step-by-step explanation:
ΔAED ~ ΔACB
[∠DAE = ∠BAC ( common angle ), [tex]\frac{AE}{AC} = \frac{AD}{AB}[/tex] ( gives a ratio 1:2 ) ]
[tex]\frac{AE}{AC} = \frac{DE}{BC}[/tex]
Since AC = 2AE [ AC = AE + EC, But AE = EC, ∴ AC = AE + AE ]
[tex]\frac{AE}{2AE} = \frac{x + 1}{4x - 6}\\\\\frac{1}{2} = \frac{x + 1}{4x - 6}\\\\\\Cross - multiplying,\\\\4x - 6 = 2 *(x + 1)\\4x - 6 = 2x + 2\\4x - 2x = 2 + 6\\2x = 8\\x = 4[/tex]
