Answer: x = 5
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Step-by-step explanation:
The alternate interior angles are congruent because of the parallel lines.
Set the angle expressions equal to each other. Solve for x.
12x+8 = 14x-2
12x+8-12x = 14x-2-12x .... subtract 12x from both sides
8 = 2x-2
8+2 = 2x-2+2 ... add 2 to both sides
10 = 2x
2x = 10
2x/2 = 10/2 ... divide both sides by 2
x = 5
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As a check, plug this x value back into the original equation. After simplifying, you should get the same number on both sides.
12*x+8 = 14*x - 2
12*5+8 = 14*5-2 ... plug in x = 5
60+8 = 70-2
68 = 68
Both angles shown are 68 degrees, so we have confirmed the answer.