Question

Complete the process of solving the equation.
Fill in all missing terms and select all missing descriptions. Simplify any fractions.
17(4x+1)+14x=–17x+17
68x+17+14x=–17x+17
Add 17 to both sides
Subtract 17 from both sides
Multiply both sides by 17
Divide both sides by 17
Apply the distributive property
___ +17=–17x+17
Combine like terms
99x+17=17
Add 17x to both sides
Subtract 17x from both sides
Multiply both sides by 17x
Divide both sides by 17x
Apply the distributive property
99x=___
Subtract 17 from both sides
x=___
Divide both sides by 99

Answer 1

Let's complete and simplify the process step by step:

1. Starting from the original equation:
\[
17(4x + 1) + 14x = -17x + 17
\]

2. Apply the distributive property to the left side:
\[
68x + 17 + 14x = -17x + 17
\]

3. Combine like terms on the left side:
\[
82x + 17 = -17x + 17
\]

4. Subtract 17 from both sides:
\[
82x = -17x
\]

5. Add \( 17x \) to both sides:
\[
82x + 17x = 0
\]
\[
99x = 0
\]

6. Subtract 17 from both sides: (Note: This step was unnecessary here but can be done if equating to a constant.)
\[
99x = 0
\]

7. Divide both sides by 99:
\[
x = 0
\]

So, the complete process including the filled in blanks and selections would look like this:

- \( 99x = 0 \)
- \( x = 0 \)

The final solution is \( x = 0 \).

Now we determine the missing descriptions:

- **Apply the distributive property**
- **Combine like terms**
- **Add 17x to both sides**
- **Divide both sides by 99**

These actions reflect the operations conducted to solve the original equation step by step.