Question

Complete the process of solving the equation.
Fill in all the missing terms and select all missing descriptions. Simplify any fractions.
4(
–
3d+14)=
–
17d+16
–
12d+56=
–
17d+16
Add 4 to both sides
Subtract 4 from both sides
Multiply both sides by 4
Divide both sides by 4
Apply the distributive property
+56=16 Add 17d to both sides
5d=
–
40
Add 56 to both sides
Subtract 56 from both sides
Multiply both sides by 56
Divide both sides by 56
Combine like terms
d=
Divide both sides by 5

Answer 1

Let's complete the step-by-step process of solving the equation given in the problem:

1. Start with the equation:
\[
4(-3d + 14) = -17d + 16
\]

2. **Apply the distributive property**: Distribute the 4 on the left side:
\[
4 \times -3d + 4 \times 14 = -17d + 16
\]
This simplifies to:
\[
-12d + 56 = -17d + 16
\]

3. Now we have:
\[
-12d + 56 = -17d + 16
\]

4. **Add 17d to both sides**:
\[
-12d + 17d + 56 = 16
\]
This simplifies to:
\[
5d + 56 = 16
\]

5. **Subtract 56 from both sides**:
\[
5d + 56 - 56 = 16 - 56
\]
This simplifies to:
\[
5d = -40
\]

6. **Divide both sides by 5**:
\[
d = \frac{-40}{5}
\]
This simplifies to:
\[
d = -8
\]

The final answer is:
\[
d = -8
\]

### Summary of Missing Descriptions
- Apply the distributive property
- Add 17d to both sides
- Subtract 56 from both sides
- Divide both sides by 5

**Final Answer**:
- \( d = -8 \)