To solve the compound inequality \(-2 < 4x - 10 < 6\), we will break it into two parts and solve each part.
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First part: \(-2 < 4x - 10\)
To isolate \(4x\), add \(10\) to both sides:
\[ -2 + 10 < 4x \] \[ 8 < 4x \]
Now divide both sides by \(4\):
\[ 2 < x \] or \[ x > 2 \]
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Second part: \(4x - 10 < 6\)
Again, add \(10\) to both sides:
\[ 4x < 6 + 10 \] \[ 4x < 16 \]
Now divide both sides by \(4\):
\[ x < 4 \]
Combining both parts, we have:
\[ 2 < x < 4 \]
Thus, the solution to the inequality \(-2 < 4x - 10 < 6\) is:
\(2 < x < 4\)
This confirms that the correct answer is indeed \(2 < x < 4\).