Complete the process of solving the equation.

Fill in all missing terms and select all missing descriptions. Simplify any fractions.

17(4q–2)+3q=

18q–13

68q+34+3q=

18q–13
Add -17 to both sides
Subtract -17 from both sides
Multiply both sides by -17
Divide both sides by -17
Apply the distributive property
+34=

18q–13
Combine like terms

47q+34=

13
Add 18q to both sides
Subtract 18q from both sides
Multiply both sides by 18q
Divide both sides by 18q
Apply the distributive property

47q=
Subtract 34 from both sides
q=
Divide both sides by

47

1 answer

To solve the equation step by step, let's follow the provided steps and fill in the missing components:

  1. Start with the original equation: \[ -17(4q - 2) + 3q = -18q - 13 \]

  2. Apply the distributive property: \[ -17 \cdot 4q + (-17) \cdot (-2) + 3q = -18q - 13 \] This simplifies to: \[ -68q + 34 + 3q = -18q - 13 \]

  3. Combine like terms on the left: \[ (-68q + 3q) + 34 = -18q - 13 \] This simplifies to: \[ -65q + 34 = -18q - 13 \]

  4. Now, add \( 18q \) to both sides: \[ -65q + 18q + 34 = -13 \] This simplifies to: \[ -47q + 34 = -13 \]

  5. Now, subtract \( 34 \) from both sides: \[ -47q = -13 - 34 \] This simplifies to: \[ -47q = -47 \]

  6. Finally, divide both sides by \( -47 \): \[ q = 1 \]

Now, filling in and indicating what actions we took based on the provided structure:

Filled Missing Terms and Descriptions:

  • After applying the distributive property: \[ -68q + 34 + 3q = -18q - 13 \]

  • Combining like terms: \[ -65q + 34 = -18q - 13 \]

  • Add \( 18q \) to both sides: \[ -47q + 34 = -13 \]

  • Subtract \( 34 \) from both sides: \[ -47q = -47 \]

  • Divide both sides by (-47): \[ q = 1 \]

So the compiled process shows how we solve for \( q \), filling in the necessary terms and describing the steps taken correctly.