Question

Complete the process of solving the equation.
Fill in all missing terms and select all missing descriptions. Simplify any fractions.
–
3(
–
7v+1)–14v=
–
10
21v–3–14v=
–
10
Add -3 to both sides
Subtract -3 from both sides
Multiply both sides by -3
Divide both sides by -3
Apply the distributive property
7v–3=
–
10
Add 21v to both sides
Subtract 21v from both sides
Multiply both sides by 21v
Divide both sides by 21v
Combine like terms
7v=
Add 3 to both sides
v=
Divide both sides by 7

Answer 1

Let's go through the process of solving the equation step-by-step, filling in all missing terms and selecting the appropriate descriptions where necessary.

1. Start from the given equation:
\[
-3(-7v + 1) - 14v = -10
\]

2. Apply the distributive property:
-3(-7v + 1) becomes 21v - 3.
Therefore, the equation rewrites to:
\[
21v - 3 - 14v = -10
\]

3. Combine like terms (21v - 14v):
\[
7v - 3 = -10
\]

4. Add 3 to both sides:
\[
7v = -10 + 3
\]
This simplifies to:
\[
7v = -7
\]

5. Divide both sides by 7:
\[
v = \frac{-7}{7}
\]
This simplifies to:
\[
v = -1
\]

So, the completed equations and operations are as follows:

1. Apply the distributive property:
\[
21v - 3 - 14v = -10
\]

2. Combine like terms:
\[
7v - 3 = -10
\]

3. Add 3 to both sides:
\[
7v = -7
\]

4. Divide both sides by 7:
\[
v = -1
\]

### Selected Descriptions:
- Apply the distributive property
- Combine like terms
- Add 3 to both sides
- Divide both sides by 7

This finalizes the process for solving the equation, obtaining the result \( v = -1 \).