Question

Complete the process of solving the equation.
Fill in all missing terms and select all missing descriptions. Simplify any fractions.
9(u+8)–10=4u+7
9u+72–10=4u+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
9u+
=4u+7
Combine like terms
5u+62=7
Add 4u to both sides
Subtract 4u from both sides
Multiply both sides by 4u
Divide both sides by 4u
Apply the distributive property
5u=
–
55
Add 62 to both sides
Subtract 62 from both sides
Multiply both sides by 62
Divide both sides by 62
Apply the distributive property
u=
Divide both sides by 5

Answer 1

Let's solve the equation step by step, filling in the missing terms and making sure to simplify any fractions.

We start with the given equation:
\[ 9(u + 8) - 10 = 4u + 7 \]

1. **Apply the distributive property:**
\[
9u + 72 - 10 = 4u + 7
\]

2. **Combine like terms (on the left side):**
\[
9u + 62 = 4u + 7
\]

3. **Subtract \(4u\) from both sides:**
\[
9u - 4u + 62 = 7
\]
Which simplifies to:
\[
5u + 62 = 7
\]

4. **Subtract \(62\) from both sides:**
\[
5u = 7 - 62
\]
Which simplifies to:
\[
5u = -55
\]

5. **Divide both sides by 5:**
\[
u = \frac{-55}{5}
\]
Which simplifies to:
\[
u = -11
\]

Here are the missing terms and descriptions to fill in the steps:

**Missing terms:**
- After "9u +": **62**
- After "5u =": **−55**
- After "u =": **−11**

**Missing descriptions:**
- After "Combine like terms": This step has already been filled in because we combined like terms in the transition to \(5u + 62 = 7\).
- The operations leading to \(5u = -55\) include **Subtract 62 from both sides**.
- The final operation to solve for \(u\) involves **Divide both sides by 5**.

### Summary of the completed process:
- Start with \(9(u + 8) - 10 = 4u + 7\)
- Apply the distributive property to get \(9u + 62 = 4u + 7\)
- Subtract \(4u\) from both sides: \(5u + 62 = 7\)
- Subtract \(62\) from both sides: \(5u = -55\)
- Divide by \(5\): \(u = -11\)