Complete the process of solving the equation.

Question

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.