Question

Complete the process of solving the equation.
Fill in all missing terms and select all missing descriptions. Simplify any fractions.
–
2c+16=c+1
–
3c+16=1
Add c to both sides
Subtract c from both sides
Multiply both sides by c
Divide both sides by c
Apply the distributive property
–
3c=
–
15
Add 16 to both sides
Subtract 16 from both sides
Multiply both sides by 16
Divide both sides by 16
Apply the distributive property
c=
Divide both sides by
–
3

Answer 1

Let's complete the process of solving the equation step by step.

Starting with the equation:
\[
-2c + 16 = c + 1
\]

1. **Add \(c\) to both sides** (to get all terms involving c on one side):
\[
-2c + c + 16 = 1
\]
This simplifies to:
\[
-1c + 16 = 1
\]

2. **Subtract 16 from both sides** (to isolate the term with c):
\[
-1c + 16 - 16 = 1 - 16
\]
This simplifies to:
\[
-1c = -15
\]

3. **Multiply both sides by -1** (to solve for c):
\[
c = 15
\]

So the complete process of solving the equation is as follows:

Start with:
\[
-2c + 16 = c + 1
\]

1. Add \(c\) to both sides:
\[
-2c + c + 16 = 1
\]

This results in:
\[
-1c + 16 = 1
\]

2. Subtract 16 from both sides:
\[
-1c = -15
\]

3. Multiply both sides by -1:
\[
c = 15
\]

Therefore, the missing terms and descriptions can be filled in as such:

- **3c =** \(-1c + 16 = 1\) (which should be adjusted to avoid confusion; the outcome is based on simplifying the previous steps)
- **15 =** \(-15\) or directly \(= -15\) from isolating \(c\)
- **Divide both sides by** \(-1\).

Thus, the complete answer is:
\[
c = 15
\]

It is also straightforward to note that:
1. "Add c to both sides" → Step 1
2. "Subtract 16 from both sides" → Step 2
3. "Divide both sides by -1" → Final calculation to isolate \(c\).

Adjust or clarify if needed for planarity in description!