Question

Complete the process of solving the equation.
Fill in all missing terms and select all missing descriptions. Simplify any fractions.
–
3(
–
4q+9)=16q–11
12q–27=16q–11
Add -3 to both sides
Subtract -3 from both sides
Multiply both sides by -3
Divide both sides by -3
Apply the distributive property
–
4q–27=
–
11
Add 16q to both sides
Subtract 16q from both sides
Multiply both sides by 16q
Divide both sides by 16q
Apply the distributive property
–
4q=
Add 27 to both sides
q=
Divide both sides by
–
4

Answer 1

Let's solve the equation step by step, filling in the missing terms and selecting the correct descriptions.

Starting with the given equation:

\[
-3(-4q + 9) = 16q - 11
\]

1. **Apply the distributive property:**
\[
-3(-4q) + (-3)(9) = 16q - 11
\]
This simplifies to:
\[
12q - 27 = 16q - 11
\]

2. **Now we have:**
\[
12q - 27 = 16q - 11
\]

3. **We want to isolate q. Start by moving all terms involving q to one side. Subtract 12q from both sides:**
\[
-27 = 16q - 12q - 11
\]
Simplifying gives:
\[
-27 = 4q - 11
\]

4. **Next, add 11 to both sides:**
\[
-27 + 11 = 4q
\]
Simplifying gives:
\[
-16 = 4q
\]

5. **Now, divide both sides by 4 to solve for q:**
\[
q = \frac{-16}{4}
\]
Simplifying gives:
\[
q = -4
\]

So, the completed process looks like this:

\[
-3(-4q + 9) = 16q - 11 \quad \text{(Original equation)}
\]
\[
12q - 27 = 16q - 11 \quad \text{(After applying the distributive property)}
\]
\[
-27 = 4q - 11 \quad \text{(After subtracting 12q from both sides)}
\]
\[
-16 = 4q \quad \text{(After adding 11 to both sides)}
\]
\[
q = -4 \quad \text{(After dividing both sides by 4)}
\]

### Fill in the missing terms and descriptions:

1. **Original Equation**
\[
-3(-4q + 9) = 16q - 11
\]

2. **Fill in the blank after applying the distributive property**
\[
12q - 27 = 16q - 11
\]
**Description:** Apply the distributive property

3. **Fill in the blank after moving q terms**
\[
-27 = 4q - 11
\]
**Description:** Subtract 12q from both sides

4. **Fill in the blank after adding 11**
\[
-16 = 4q
\]
**Description:** Add 11 to both sides

5. **Final result**
\[
q = -4
\]
**Description:** Divide both sides by 4

### Missing Descriptions:
- Apply the distributive property
- Subtract 12q from both sides
- Add 11 to both sides
- Divide both sides by 4

Thus, the solution is \( q = -4 \).