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Answer

The solution to the compound inequality is -2 \leqslant x < 2.

Explanation

To solve the compound inequality -4\leqslant 4x+4\lt 12, we need to isolate x in the middle. We can do this by first subtracting 4 from all three parts of the inequality. This gives us -4 - 4 \leqslant 4x + 4 - 4 < 12 - 4, which simplifies to -8 \leqslant 4x < 8. Then, we divide all three parts of the inequality by 4 to solve for x. This gives us -8/4 \leqslant 4x/4 < 8/4, which simplifies to -2 \leqslant x < 2. To graph this solution on the number line, we make a filled circle at -2 (because -2 is included in the solution) and an open circle at 2 (because 2 is not included in the solution). Then, we draw a line connecting the two circles to represent all the numbers in between.

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