<h3>Given</h3>
DP = 3x+2
DE = 10x-12
P is the midpoint of DE
<h3>Find</h3>
DP
<h3>Solution</h3>
If P is the midpoint, then PE = DP. The parts of a line segment add up to give the length of the entire line segment:
... DP + PE = DE
... DP + DP = DE . . . . . . use DP = PE
... 2(DP) = DE . . . . . . . . simplify
... 2(3x + 2) = 10x - 12 . . substitute the given in formation
... 16 = 4x . . . . . . . . . . . . add -6x +12
... 4 = x . . . . . . . . . . . . . . divide by the coefficient of x
The length of DP is 3×4 +2 = 14
<u>Check</u>
The length of DE is 10×4 - 12 = 28, which is 2 times the length of DP
