Complete the process of solving the equation.

Question

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:

• \( d = -8 \)