Answer:
[tex] 4x + 8 + 27 = 6x [/tex], [tex] x = 17.5 [/tex]
Step-by-step explanation:
LM = 4x + 8
MN = 27
LN = 6x
Points L, M, and N are collinear, therefore,
[tex] LM + MN = LN [/tex] (segment addition postulate)
Thus, the equation that would be set up to solve for x would be:
[tex] 4x + 8 + 27 = 6x [/tex] (substitution)
Solve for x as follows:
[tex] 4x + 35 = 6x [/tex]
Subtract 4x from both sides
[tex] 4x + 35 - 4x = 6x - 4x [/tex]
[tex] 35 = 2x [/tex]
Divide both sides by 2
[tex] \frac{35}{2} = \frac{2x}{2} [/tex]
[tex] 17.5 = x [/tex]
[tex] x = 17.5 [/tex]
