From the given information, we can deduce that BD is the average of AC and CE. Hence, we have
BD = (AC + CE)/2
Plugging in the given expressions for BD, AC, and CE, we get:
3x + 5 = (AC + CE)/2
We also know that AE = AC + CE. Plugging in the given expression for AE, we get:
4x + 20 = AC + CE
Now, we have two equations:
3x + 5 = (AC + CE)/2
4x + 20 = AC + CE
To solve for x, we can subtract the first equation from the second equation:
(4x + 20) - (3x + 5) = (AC + CE) - ((AC + CE)/2)
x + 15 = (AC + CE)/2
Multiplying both sides by 2, we get:
2x + 30 = AC + CE
Now, we can substitute this expression into the first equation:
3x + 5 = (2x + 30)/2
Multiplying both sides by 2, we get:
6x + 10 = 2x + 30
Subtracting 2x and 10 from both sides, we get:
4x = 20
Dividing both sides by 4, we get:
x = 5
Therefore, x = 5.
B is the midpoint of modifying above A C with barand D is the midpoint of modifying above C E with bar. Solve for x, given BD = 3x + 5 and AE = 4x + 20.
The figure shows triangle A C E with a segment B D connecting the sides. point B is on segment A C. point D is on segment C E.
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