If it's a rhombus then FE = ED = DG = GF.
Therefore
2x + 2 = 4x - 8 and 2x + 2 = 12 and 4x - 8 = 12
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2x + 2 = 4x - 8 subtract 2 from both sides
2x = 4x - 10 subtract 4x from both sides
-2x = -10 divide both sides by (-2)
x = 5
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2x + 2 = 12 subtract 2 from both sides
2x = 10 divide both sides by 2
x = 5
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4x - 8 = 12 add 8 to both sides
4x = 20 divide both sides by 4
x = 5
It's the rhombus!
Answer: x = 5