To solve the equation \( 2|2x + 3| = 10 \), we first isolate the absolute value:
\[ |2x + 3| = \frac{10}{2} = 5 \]
Now we have two cases to consider because of the absolute value:
Case 1: \[ 2x + 3 = 5 \] Subtracting 3 from both sides: \[ 2x = 5 - 3 \] \[ 2x = 2 \] Dividing by 2: \[ x = 1 \]
Case 2: \[ 2x + 3 = -5 \] Subtracting 3 from both sides: \[ 2x = -5 - 3 \] \[ 2x = -8 \] Dividing by 2: \[ x = -4 \]
Therefore, we have the solutions: \[ x = 1 \quad \text{and} \quad x = -4 \]
The smaller \( x \) value is \( -4 \) and the larger is \( 1 \).
So, filling in the boxes:
\( x = (-4) \) or \( x = (1) \)