Answer:
[tex] x = 4 [/tex]
Step-by-step explanation:
[tex] GH = 3x [/tex] (given)
[tex] HJ = x + 16 [/tex] (given)
[tex] GJ = 32 [/tex] (given)
[tex] GH + HJ = GJ [/tex] (segment addition postulate)
[tex] (3x) + (x + 16) = 32 [/tex] (substitution)
Solve for x
[tex] 3x + x + 16 = 32 [/tex]
[tex] 4x + 16 = 32 [/tex]
[tex] 4x + 16 - 16 = 32 - 16 [/tex] (subtraction property of equality)
[tex] 4x = 16 [/tex]
[tex] \frac{4x}{4} = \frac{16}{4} [/tex] (division property of equality)
[tex] x = 4 [/tex]
