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To find the value of x, we can use the property of intersecting chords in a circle.
According to the property, when two chords intersect inside a circle, the products of their segments are equal.
So, in this case, we have AE × EB = CE × ED.
Given AE = 3 and EB = 4, we can substitute these values:
3 × 4 = CE × (x-4)
12 = CE × (x-4)
Now, we have an equation we can solve for x.
To do this, we can expand the right side:
12 = CE × x - 4CE
Next, let's gather the x terms on one side and the constant terms on the other side:
CE × x = 4CE + 12
Now, we can factor out CE on the right side:
CE × x = CE × (4 + 12/CE)
Dividing both sides of the equation by CE, we get:
x = 4 + 12/CE
So, the value of x is 4 plus 12 divided by CE.