To solve the compound inequality \(-12 \leq 2x - 4 < 10\), we'll break it into two parts and solve each part separately.
Step 1: Solve the left side of the inequality:
\[ -12 \leq 2x - 4 \]
Add 4 to both sides:
\[ -12 + 4 \leq 2x \] \[ -8 \leq 2x \]
Now, divide by 2:
\[ -4 \leq x \]
or
\[ x \geq -4 \]
Step 2: Solve the right side of the inequality:
\[ 2x - 4 < 10 \]
Add 4 to both sides:
\[ 2x < 10 + 4 \] \[ 2x < 14 \]
Now, divide by 2:
\[ x < 7 \]
Combining the results:
From the left side, we have \(x \geq -4\), and from the right side, we have \(x < 7\).
So the combined solution is:
\[ -4 \leq x < 7 \]
In interval notation, this is:
\[ [-4, 7) \]