explain why there must be at least two lines on any given
plane,

there must be at least two lines on any plane because a plane is defined by 3 non-collinear points. Explanation: ... These lines may or may not intersect. If two of the 3 points are collinear, then we have a line through those 2 points as well as a line through the 3rd point.

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.