Let's solve the equation step by step and fill in the missing terms.
We start with the original equation: \[ -5(-4w + 7) = 17w - 20 \]
- 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: \[ 20w - 35 = 17w - 20 \]
-
Subtract 17w from both sides: \[ 20w - 17w - 35 = -20 \] This simplifies to: \[ 3w - 35 = -20 \]
-
Add 35 to both sides: \[ 3w - 35 + 35 = -20 + 35 \] This simplifies to: \[ 3w = 15 \]
-
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:
- \(3w - 35 = -20\)
- \(3w = 15\)
- \(w = 5\)
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.