Complete the process of solving the equation.

Question

Fill in all missing terms and select all missing descriptions. Simplify any fractions.
–
3(14c+4)+5=
–
12c–7
–12+5=
–
12c–7
Add -3 to both sides
Subtract -3 from both sides
Multiply both sides by -3
Divide both sides by -3
Apply the distributive property
–
42c–
=
–
12c–7
Add -12 to both sides
Subtract -12 from both sides
Multiply both sides by -12
Divide both sides by -12
Combine like terms
–7=
–
7
Add 12c to both sides
Subtract 12c from both sides
Multiply both sides by 12c
Divide both sides by 12c
Apply the distributive property
–
30c=
Add 7 to both sides
Subtract 7 from both sides
Multiply both sides by 7
Divide both sides by 7
Apply the distributive property
c=
Add -30 to both sides
Subtract -30 from both sides
Multiply both sides by -30
Divide both sides by -30
Combine like terms

Answer 1

Let's break down the equation \( -3(14c+4)+5= -12c-7 \) step by step and fill in all the missing terms and descriptions.

1. Start with the original equation: \[ -3(14c+4)+5= -12c-7 \]

2. Apply the distributive property: \[ -42c - 12 + 5 = -12c - 7 \]

3. Combine like terms: \[ -42c - 7 = -12c - 7 \]

4. Next, we can add 7 to both sides: \[ -42c = -12c \]

5. Now, add \(12c\) to both sides: \[ -42c + 12c = 0 \] Which simplifies to: \[ -30c = 0 \]

6. Next, divide both sides by \(-30\): \[ c = 0 \]

Now, we can piece together the explanations and steps filled in:

• Apply the distributive property (Step where we apply \(-3\) to \(14c\) and \(4\))
• Combine like terms (Combining \(-12\) and \(5\))
• Add \(7\) to both sides (getting rid of the \(-7\) on the right side)
• Add \(12c\) to both sides (moving \(-12c\) from the right to the left)
• Divide both sides by \(-30\) (to isolate \(c\))

So the missing answers would be:

1. \(42c-\) (completed term)
2. \(12c-7\) (completed term)
3. Add 7 to both sides (correct operation)
4. Subtract 12c from both sides (correct operation)
5. Combine like terms (correct operation)
6. \(c=\) (completed term)
7. Divide both sides by \(-30\) (correct operation)

This completes the solving process correctly and fully. The final solution stated that \(c = 0\).

Answer 2

The answer is:
–3(14c+4)+5=–12c–7
-42c–12+5=–12c–7
Apply the distributive property
–42c–7=–12c–7
Combine like terms
-30c–7=–7
Add 12c to both sides
–30c=0
Add 7 to both sides
c=0
Divide both sides by -30

Answer 3

Thank you for your patience! Let's clarify the steps to solve the equation \( -3(14c + 4) + 5 = -12c - 7 \) more accurately, incorporating your feedback into a detailed solution sequence.

1. Starting Equation: \[ -3(14c + 4) + 5 = -12c - 7 \]

2. Apply the Distributive Property: \[ -42c - 12 + 5 = -12c - 7 \]

3. Combine Like Terms: \[ -42c - 7 = -12c - 7 \]

4. Add \(12c\) to Both Sides: \[ -42c + 12c - 7 = -7 \] This simplifies to: \[ -30c - 7 = -7 \]

5. Add \(7\) to Both Sides: \[ -30c = 0 \]

6. Divide Both Sides by \(-30\): \[ c = 0 \]

In a structured format, the filled steps with descriptions are:

• \( -3(14c + 4) + 5 = -12c - 7 \)
• \( -42c - 12 + 5 = -12c - 7 \)
• Apply the distributive property
• \( -42c - 7 = -12c - 7 \)
• Combine like terms
• \( -30c - 7 = -7 \)
• Add \(12c\) to both sides
• \( -30c = 0 \)
• Add \(7\) to both sides
• \( c = 0 \)
• Divide both sides by \(-30\)

This structure captures the mathematical process accurately and clearly. Thank you for providing the correct direction for the sequence! The key result is \( c = 0 \).