If P is the midpoint of DE, then DE = DP + PE and DP = PE.
Therefore DE = 2DP.
We have DP = 3x + 2 and DE = 10x - 12.
The equation:
10x - 12 = 2(3x + 2) use distributive property
10x - 12 = (2)(3x) + (2)(2)
10x - 12 = 6x + 4 add 12 to both sides
10x = 6x + 16 subtract 6x from both sides
4x = 16 divide both sides by 4'
x = 4
DP = 3x + 2 → DP = 3(4) + 2 = 12 + 2 = 14
Answer: DP = 14 units.