Complete the process of solving the equation.

Question

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.