Answer: UV = 52
Concept:
Additive property of length, or the segment addition postulate, states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Solve:
<u>Given information</u>
TU = 4x
UV = 2x + 14
TV = 7x - 5
<u>Given expression deducted from the additive property of length</u>
TV = TU + UV
<u>Substitute values into the expression</u>
7x - 5 = 4x + 2x + 14
<u>Combine like terms</u>
7x - 5 = 6x + 14
<u />
<u>Subtract 6x on both sides</u>
7x - 5 - 6x = 6x + 14 - 6x
x - 5 = 14
<u>Add 5 on both sides</u>
x - 5 + 5 = 14 + 5
x = 19
<u>Find UV by substituting the value of x</u>
UV = 2x + 14 = 2 (19) + 14 = 
Hope this helps!! :)
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Answer:
equation of line: y = 2x + 5
Explanation:
using the formula:
2(4x + 2) = 4x - 12(x - 1) |use distributive property: a(b +/- c) = ab +/- ac
8x + 4 = 4x - 12x + 12
8x + 4 = -8x + 12 |subtract 4 from both sides
8x = -8x + 8 |add 8x to both sides
16x = 8 |divide both sides by 16
x = 0.5