Question

Complete the process of solving the equation.
Fill in all missing terms and select all missing descriptions. Simplify any fractions.
–
5c+12+10c=6c+19
5c+12=6c+19
Add -5c to both sides
Subtract -5c from both sides
Multiply both sides by -5c
Divide both sides by -5c
Combine like terms
+12=19 Subtract 6c from both sides
–
c=7
Add 12 to both sides
Subtract 12 from both sides
Multiply both sides by 12
Divide both sides by 12
Apply the distributive property
c=
Divide both sides by
–
1

Answer 1

Let's solve the equation step by step and fill in all missing terms and descriptions.

The original equation is:

\[
-5c + 12 + 10c = 6c + 19
\]

Begin by combining like terms on the left side:

\[
(10c - 5c) + 12 = 6c + 19
\]

This simplifies to:

\[
5c + 12 = 6c + 19
\]

Next, we will isolate \(c\). The first step will be to subtract \(6c\) from both sides:

\[
5c + 12 - 6c = 19
\]

This gives:

\[
-1c + 12 = 19
\]

or

\[
-1c + 12 = 19
\]

Next, we will subtract 12 from both sides to isolate the term with \(c\):

\[
-1c = 19 - 12
\]

This simplifies to:

\[
-1c = 7
\]

Now, we divide both sides by \(-1\):

\[
c = \frac{7}{-1}
\]

This simplifies to:

\[
c = -7
\]

So, the complete steps will be as follows:

1. Start with the equation:
\[
5c + 12 + 10c = 6c + 19
\]

2. Combine like terms:
\[
(10c - 5c) + 12 = 6c + 19 \implies 5c + 12 = 6c + 19
\]

3. Subtract \(6c\) from both sides:
\[
5c - 6c + 12 = 19 \implies -1c + 12 = 19
\]

4. Subtract 12 from both sides:
\[
-1c = 7
\]

5. Divide both sides by \(-1\):
\[
c = -7
\]

Thus, the value of \(c\) is:

\[
c = -7
\]

To summarize the missing descriptions and terms filled in:
- Combine like terms
- Subtract \(6c\) from both sides
- Subtract 12 from both sides
- Divide both sides by -1