Complete the process of solving the equation.

Question

Fill in all missing terms and select all missing descriptions. Simplify any fractions.
–
9(
–
8q–7)–7q=9q+7
+63–7q=9q+7
Add -9 to both sides
Subtract -9 from both sides
Multiply both sides by -9
Divide both sides by -9
Apply the distributive property
+63=9q+7
Add 72q to both sides
Subtract 72q from both sides
Multiply both sides by 72q
Divide both sides by 72q
Combine like terms
+63=7
Add 9q to both sides
Subtract 9q from both sides
Multiply both sides by 9q
Divide both sides by 9q
Apply the distributive property
56q=
Add 63 to both sides
Subtract 63 from both sides
Multiply both sides by 63
Divide both sides by 63
Apply the distributive property
q=
Add 56 to both sides
Subtract 56 from both sides
Multiply both sides by 56
Divide both sides by 56
Combine like terms

Answer 1

Let's solve the equation step-by-step, filling in the missing terms and descriptions as we go along:

1. Start with the original equation: \[ -9(-8q - 7) - 7q = 9q + 7 \]

2. Apply the distributive property: \[ -9 \cdot -8q - 9 \cdot -7 - 7q = 9q + 7 \] This simplifies to: \[ 72q + 63 - 7q = 9q + 7 \]

3. Combine like terms on the left side: \[ (72q - 7q) + 63 = 9q + 7 \] Which simplifies to: \[ 65q + 63 = 9q + 7 \]

4. Next, subtract \(9q\) from both sides: \[ 65q - 9q + 63 = 7 \] This simplifies to: \[ 56q + 63 = 7 \]

5. Now, subtract \(63\) from both sides: \[ 56q + 63 - 63 = 7 - 63 \] This simplifies to: \[ 56q = -56 \]

6. Finally, divide both sides by \(56\): \[ q = \frac{-56}{56} \] So: \[ q = -1 \]

Summary of Steps and Missing Descriptions:

1. Apply the distributive property
2. Combine like terms
3. Subtract \(9q\) from both sides
4. Subtract \(63\) from both sides
5. Divide both sides by \(56\)

The complete solution is \(q = -1\).