Let's solve the equations step by step while applying the appropriate algebraic operations.
The First Equation
The first equation you provided is: \[ -2(-7p - 18) - 18p = -20 \]
Step 1: Apply the Distributive Property Distributing \(-2\) into the expression gives: \[ 14p + 36 - 18p = -20 \]
Step 2: Combine Like Terms Combine \(14p\) and \(-18p\): \[ (14p - 18p) + 36 = -20 \] This simplifies to: \[ -4p + 36 = -20 \]
Step 3: Subtract 36 from Both Sides \[ -4p + 36 - 36 = -20 - 36 \] This gives: \[ -4p = -56 \]
Step 4: Divide Both Sides by -4 \[ p = \frac{-56}{-4} = 14 \]
The Second Equation
The second equation is: \[ 14p + 36 - 18p = -20 \]
Step 1: Combine Like Terms Combine \(14p\) and \(-18p\): \[ (14p - 18p) + 36 = -20 \] This simplifies to: \[ -4p + 36 = -20 \]
Step 2: Subtract 36 from Both Sides \[ -4p + 36 - 36 = -20 - 36 \] This gives: \[ -4p = -56 \]
Step 3: Divide Both Sides by -4 \[ p = \frac{-56}{-4} = 14 \]
Both equations lead us to the same solution: \[ \boxed{14} \]