The value of x is 3. The methods used in justifying each step are listed below
a) Addition of line segments
b) Substitution rule
c) Simplification by addition of like terms
d) Collecting lie terms
e) Dividing both sides by 8
AB = 2x
BC = 6x + 8
AC = 32
AB + BC = AC (Addition rule)
Addition of the component segments of a line
2x + 6x + 8 = 32 (Substitution rule)
Substituting for AB, BC, and AC in the equation AB + BC = AC
8x + 8 = 32 (Simplification)
Simplifying 2x + 6x + 8 = 32 by adding like terms
8x = 24 (Collecting like terms)
8x = 32 - 8
8x = 24
x = 3 (Divide both sides by 8)
8x / 8 = 24/8
x = 3
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