To solve the compound inequality \(-2 < 4x - 10 < 6\), we can break it down into two inequalities and solve each part separately.
Step 1: Solve the left inequality
\(-2 < 4x - 10\)
Add 10 to both sides:
\(-2 + 10 < 4x\)
This simplifies to:
\(8 < 4x\)
Now, divide both sides by 4:
\(\frac{8}{4} < x\)
Which gives:
\(2 < x\) or equivalently \(x > 2\).
Step 2: Solve the right inequality
\(4x - 10 < 6\)
Add 10 to both sides:
\(4x < 6 + 10\)
This simplifies to:
\(4x < 16\)
Now, divide both sides by 4:
\(x < \frac{16}{4}\)
Which gives:
\(x < 4\).
Step 3: Combine the results
From the two parts, we have:
\(2 < x < 4\)
So the solution to the compound inequality \(-2 < 4x - 10 < 6\) is:
\(\boxed{2 < x < 4}\).