Solutions

1. \(-1\)


2. \(-8\) (Written Solution)

   We do the order of operations backwards to solve for \({\text{W}}\).

   Step 1: Combine like terms using addition or subtraction. Right now we have terms containing \({\text{W}}\) on both sides of the equation:

   \(12 + 3{\text{W}} = -4 + {\text{W}}\)

   First, we’ll subtract W from both sides to gather all terms containing W to the left side of the equation:

   

   Which gives us:

   \(12 + 2{\text{W}} = -4 {\color{Red} + 0}\)

   Which is equal to:

   \(12 + 2{\text{W}} = -4\)

   Next, we’ll subtract 12 from both sides of the equation:

   

   Which gives us:

   \(2{\text{W}} = {\color{Red} - 16}\)

   Step 2: Undo any multiplication using the multiplicative inverse or division to isolate \({\text{W}}\).

   \({\color{Cyan} \left [ \frac{1}{2} \right ]}2{\text{W}}=-16{\color{Cyan} \left [ \frac{1}{2} \right ]}\)

   On the left side of the equation: \(\left (\frac{1}{2} \right )\left ( 2 \right )\) gives us \(1{\text{W}}\).

   On the right side of the equation: \(-16\frac{1}{2}=\frac{-16}{1}\times\frac{1}{2}=\frac{-16\times1}{1\times2}=\frac{-16}{2}=-8\)

   So our final answer is:

   \({\text{W}} = {\color{Red} - 8}\)



3. 0 (Solution Video | Transcript)


4. \(-9\) (Written Solution)

   We do the order of operations backwards to solve for \({\text{W}}\).

   Step 1: Combine like terms using addition or subtraction.

   Right now we have terms containing \({\text{P}}\) on both sides of the equation:

   \(3 - 6{\text{P}} = -6 - 7{\text{P}}\)

   First, we’ll add \(7{\text{P}}\) to both sides to gather all terms containing \({\text{P}}\) to the left side of the equation:

   

   Which gives us:

   

   Next, we’ll subtract 3 from both sides of the equation:

   

   Which gives us:

   \({\text{P}} = {\color{Red} -9}\)



5. 4


6. \(-4\) (Solution Video | Transcript)