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

1 answer

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.