Question

Complete the process of solving the equation.
Fill in all missing terms and select all missing descriptions. Simplify any fractions.
–
5(
–
4w+7)=17w–20
20w–35=17w–20
Add -5 to both sides
Subtract -5 from both sides
Multiply both sides by -5
Divide both sides by -5
Apply the distributive property
3w–35=
–
20
Add 17w to both sides
Subtract 17w from both sides
Multiply both sides by 17w
Divide both sides by 17w
Apply the distributive property
3w=
Add 35 to both sides
w=
Divide both sides by 3

Answer 1

Let's solve the equation step by step and fill in the missing terms.

We start with the original equation:
\[
-5(-4w + 7) = 17w - 20
\]

1. **Apply the distributive property**:
\[
-5 \cdot -4w + -5 \cdot 7 = 17w - 20
\]
This gives us:
\[
20w - 35 = 17w - 20
\]

So, the first part we fill in is:
\[
\text{Apply the distributive property}
\]
and we rewrite the equation:
\[
20w - 35 = 17w - 20
\]

2. **Subtract 17w from both sides**:
\[
20w - 17w - 35 = -20
\]
This simplifies to:
\[
3w - 35 = -20
\]

3. **Add 35 to both sides**:
\[
3w - 35 + 35 = -20 + 35
\]
This simplifies to:
\[
3w = 15
\]

4. **Divide both sides by 3**:
\[
w = \frac{15}{3}
\]
This simplifies to:
\[
w = 5
\]

Now we can fill in all the missing descriptions and terms:

1. \(3w - 35 = -20\)
2. \(3w = 15\)
3. \(w = 5\)

Putting it all together, here are the filled phrases:
- Apply the distributive property to get \(20w - 35 = 17w - 20\).
- Subtract \(17w\) from both sides to get \(3w - 35 = -20\).
- Add \(35\) to both sides to get \(3w = 15\).
- Divide both sides by \(3\) to find \(w = 5\).

So the missing terms would be filled as follows:
\[
3w - 35 = -20
\]
\[
3w = 15
\]
\[
w = 5
\]

And all the operations have been simplified.