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Basic Proportionality theorem could be used to justify that equidistant from the two outside rays.
<h3>What is Basic Proportionality Theorem?</h3>
Thales's theorem, basic proportionality theorem or side splitter theorem is an important theorem in elementary geometry about the ratios of various line segments that are created if two intersecting lines are intercepted by a pair of parallels.
Here, Given that XW bisects AXZ
Thus, Basic Proportionality theorem could be used to justify that equidistant from the two outside rays.
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M= (x+n)/p
Mp= x + n
x= n - Mp
( x² - 1 ) / ( x² + 5 x + 4 ) < 0
x² + 5 x + 4 = x² + 4 x + x + 4 = x ( x + 4 ) + ( x + 4 ) = ( x + 4 ) ( x + 1 )
Therefore:
( x - 1 ) ( x + 1 ) / ( x + 4 ) ( x + 1 ) < 0
( x -1 ) / ( x + 4 ) < 0
1.
x - 1 > 0 and x + 4 < 0
x > 1 and x < - 4 ( not possible )
2.
x - 1 < 0 and x + 4 > 0
x < 1 and x > - 4
Answer: x ∈ ( - 4, 1 ).
12 is the gcf of 12 and 48