Complete the process of solving the equation.

Question

Fill in all missing terms and select all missing descriptions. Simplify any fractions.
3(9w–1)=10w–3
27w–
=10w–3
Add 3 to both sides
Subtract 3 from both sides
Multiply both sides by 3
Divide both sides by 3
Apply the distributive property
–3=
–
3
Add 10w to both sides
Subtract 10w from both sides
Multiply both sides by 10w
Divide both sides by 10w
Apply the distributive property
17w=
Add 3 to both sides
Subtract 3 from both sides
Multiply both sides by 3
Divide both sides by 3
Apply the distributive property
w=
Add 17 to both sides
Subtract 17 from both sides
Multiply both sides by 17
Divide both sides by 17
Combine like terms

Answer 1

Let's solve the equation step by step, filling in the missing terms and descriptions:

1. Start with the equation:
   \(3(9w - 1) = 10w - 3\)

2. Apply the distributive property:
   \(3 \cdot 9w - 3 \cdot 1 = 10w - 3\)
   This simplifies to:
   \(27w - 3 = 10w - 3\)

3. Add 3 to both sides:
   \(27w - 3 + 3 = 10w - 3 + 3\)
   This simplifies to:
   \(27w = 10w\)

4. Subtract \(10w\) from both sides:
   \(27w - 10w = 10w - 10w\)
   This simplifies to:
   \(17w = 0\)

5. Now, divide both sides by 17:
   \(\frac{17w}{17} = \frac{0}{17}\)
   This simplifies to:
   \(w = 0\)

Now, summarizing the steps with the correct terms and descriptions:

• Apply the distributive property: \(3(9w - 1)\) becomes \(27w - 3\)
• Add 3 to both sides: \(27w - 3 + 3 = 10w - 3 + 3\)
• Subtract \(10w\) from both sides: \(27w - 10w = 10w - 10w\)
• Divide both sides by 17: \(w = 0\)

Thus, the solution to the equation is \(w = 0\).

Answer 2

The answer is:
3(9w–1)=10w–3
27w–3=10w–3
Apply the distributive property
17w–3=–3
Subtract 10w from both sides
17w=0
Add 3 to both sides
w=0
Divide both sides by 17

Answer 3

Thank you for your input. Let's correctly line up the answer step by step while capturing your response with the appropriate context:

1. Start with the equation:
   \(3(9w - 1) = 10w - 3\)

2. Apply the distributive property:
   \(3 \cdot 9w - 3 \cdot 1 = 10w - 3\)
   This simplifies to:
   \(27w - 3 = 10w - 3\)

3. Rewrite:
   \(27w - 3 = 10w - 3\)

4. Subtract \(10w\) from both sides:
   \(27w - 10w - 3 = -3\)
   This simplifies to:
   \(17w - 3 = -3\)

5. Add 3 to both sides:
   \(17w - 3 + 3 = -3 + 3\)
   This simplifies to:
   \(17w = 0\)

6. Finally, divide both sides by 17:
   \(\frac{17w}{17} = \frac{0}{17}\)
   This leads to:
   \(w = 0\)

So, your structured answer is correct, and the full process involved is:

1. Apply the distributive property: \(3(9w - 1) = 27w - 3\)
2. Equation after distribution: \(27w - 3 = 10w - 3\)
3. Subtract \(10w\) from both sides: \(17w - 3 = -3\)
4. Add 3 to both sides: \(17w = 0\)
5. Divide both sides by 17: \(w = 0\)

The solution is \(w = 0\). Thank you for your patience, and I hope this reflects the steps accurately!