Question

2(
–
10p–20)+16p=5p–4
–
20p–40+16p=5p–4
Add 2 to both sides
Subtract 2 from both sides
Multiply both sides by 2
Divide both sides by 2
Apply the distributive property
–40=5p–4
Combine like terms
–
9p–40=
–
4
Add 5p to both sides
Subtract 5p from both sides
Multiply both sides by 5p
Divide both sides by 5p
Apply the distributive property
–
9p=
Add 40 to both sides
p

Answer 1

Let's go through the equation step by step, starting with the original equation:

\[2(-10p - 20) + 16p = 5p - 4.\]

### Step 1: Apply the Distributive Property

Distributing on the left side:

\[2(-10p) + 2(-20) + 16p = 5p - 4.\]

This simplifies to:

\[-20p - 40 + 16p = 5p - 4.\]

### Step 2: Combine Like Terms on the Left Side

Combine \(-20p\) and \(16p\):

\[-20p + 16p - 40 = 5p - 4.\]

This becomes:

\[-4p - 40 = 5p - 4.\]

### Step 3: Isolate the Variable

Next, we want to isolate \(p\). Let's add \(4p\) to both sides:

\[-40 = 5p + 4p - 4,\]

which simplifies to:

\[-40 = 9p - 4.\]

### Step 4: Add 4 to Both Sides

Now, we add 4 to both sides:

\[-40 + 4 = 9p - 4 + 4,\]

which gives:

\[-36 = 9p.\]

### Step 5: Divide by 9

To solve for \(p\), divide both sides by 9:

\[\frac{-36}{9} = p,\]

which simplifies to:

\[p = -4.\]

### Conclusion

The solution to the equation is:

\[p = -4.\]