Complete the process of solving the equation.

Question

Fill in all missing terms and select all missing descriptions. Simplify any fractions.
20(
–
4w–4)=11w+11
–
80w–80=11w+11
Add 20 to both sides
Subtract 20 from both sides
Multiply both sides by 20
Divide both sides by 20
Apply the distributive property
–80=11 Subtract 11w from both sides
–
91w=91
Add 80 to both sides
Subtract 80 from both sides
Multiply both sides by 80
Divide both sides by 80
Apply the distributive property
w=
Divide both sides by
–
91

Answer 1

Let's go through the solving process step-by-step and fill in the missing terms and descriptions.

1. Start with the original equation: \[ 20(-4w - 4) = 11w + 11 \]

2. Apply the distributive property: \[ 20(-4w) + 20(-4) = 11w + 11 \] This simplifies to: \[ -80w - 80 = 11w + 11 \]

3. Now we have: \[ -80w - 80 = 11w + 11 \] Next, we will add 80 to both sides: \[ -80w = 11w + 11 + 80 \] This simplifies to: \[ -80w = 11w + 91 \]

4. Now, subtract \(11w\) from both sides: \[ -80w - 11w = 91 \] This simplifies to: \[ -91w = 91 \]

5. Now we will divide both sides by \(-91\): \[ w = \frac{91}{-91} \]

6. Finally, simplify the fraction: \[ w = -1 \]

Here is the complete process with all missing terms filled in:

1. Start with the equation: \(20(-4w - 4) = 11w + 11\)
2. Apply the distributive property: \(-80w - 80 = 11w + 11\)
3. Add 80 to both sides: \(-80w = 11w + 91\)
4. Subtract \(11w\) from both sides: \(-91w = 91\)
5. Divide both sides by \(-91\): \(w = -1\)

Final answer: \[ w = -1 \]