To solve the equation \( 2|2x + 3| = 10 \), we can first divide both sides by 2:
\[ |2x + 3| = 5 \]
Next, we'll set up two cases based on the definition of absolute value:
Case 1: \[ 2x + 3 = 5 \] Subtracting 3 from both sides: \[ 2x = 2 \] Dividing by 2: \[ x = 1 \]
Case 2: \[ 2x + 3 = -5 \] Subtracting 3 from both sides: \[ 2x = -8 \] Dividing by 2: \[ x = -4 \]
Now we have two solutions: \( x = 1 \) and \( x = -4 \).
Putting the smaller value in the first box, we have: \[ x = -4 \] or \[ x = 1 \]
So the final answers are:
- First box: \(-4\)
- Second box: \(1\)