Question

Complete the process of solving the equation.
Fill in all missing terms and select all missing descriptions. Simplify any fractions.
–
17(4q–2)+3q=
–
18q–13
–
68q+34+3q=
–
18q–13
Add -17 to both sides
Subtract -17 from both sides
Multiply both sides by -17
Divide both sides by -17
Apply the distributive property
+34=
–
18q–13
Combine like terms
–
47q+34=
–
13
Add 18q to both sides
Subtract 18q from both sides
Multiply both sides by 18q
Divide both sides by 18q
Apply the distributive property
–
47q=
Subtract 34 from both sides
q=
Divide both sides by
–
47

Answer 1

To solve the equation step by step, let's follow the provided steps and fill in the missing components:

1. Start with the original equation:
\[
-17(4q - 2) + 3q = -18q - 13
\]

2. Apply the distributive property:
\[
-17 \cdot 4q + (-17) \cdot (-2) + 3q = -18q - 13
\]
This simplifies to:
\[
-68q + 34 + 3q = -18q - 13
\]

3. Combine like terms on the left:
\[
(-68q + 3q) + 34 = -18q - 13
\]
This simplifies to:
\[
-65q + 34 = -18q - 13
\]

4. Now, add \( 18q \) to both sides:
\[
-65q + 18q + 34 = -13
\]
This simplifies to:
\[
-47q + 34 = -13
\]

5. Now, subtract \( 34 \) from both sides:
\[
-47q = -13 - 34
\]
This simplifies to:
\[
-47q = -47
\]

6. Finally, divide both sides by \( -47 \):
\[
q = 1
\]

Now, filling in and indicating what actions we took based on the provided structure:

**Filled Missing Terms and Descriptions:**

- **After applying the distributive property:**
\[
-68q + 34 + 3q = -18q - 13
\]

- **Combining like terms:**
\[
-65q + 34 = -18q - 13
\]

- **Add \( 18q \) to both sides:**
\[
-47q + 34 = -13
\]

- **Subtract \( 34 \) from both sides:**
\[
-47q = -47
\]

- **Divide both sides by (-47):**
\[
q = 1
\]

So the compiled process shows how we solve for \( q \), filling in the necessary terms and describing the steps taken correctly.