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Solve the following equation for x. Express your answer in the simplest form. 4+6(-8x+8)=4(9x-5)+5

Solve the following equation for x x . Express your answer in the simplest form.\newline4+6(−8x+8)=4(9x−5)+5 4+6(-8 x+8)=4(9 x-5)+5 \newline

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Full solution

Q. Solve the following equation for x x . Express your answer in the simplest form.\newline4+6(−8x+8)=4(9x−5)+5 4+6(-8 x+8)=4(9 x-5)+5 \newline
  1. Distribute 66: Distribute 66 into (−8x+8)(-8x+8) to get −48x+48-48x + 48.
  2. Distribute 44: Distribute 44 into (9x−5)(9x-5) to get 36x−2036x - 20.
  3. Write equation after distribution: Write the equation after distribution: 4−48x+48=36x−20+54 - 48x + 48 = 36x - 20 + 5.
  4. Combine like terms on right side: Combine like terms on the right side: 36x−20+536x - 20 + 5 becomes 36x−1536x - 15.
  5. Combine like terms on left side: Combine like terms on the left side: 4+484 + 48 becomes 5252, so we have 52−48x=36x−1552 - 48x = 36x - 15.
  6. Add 48x48x to both sides: Add 48x48x to both sides to get 52=84x−1552 = 84x - 15.
  7. Add 1515 to both sides: Add 1515 to both sides to get 67=84x67 = 84x.
  8. Divide both sides: Divide both sides by 8484 to solve for xx: x=6784x = \frac{67}{84}.
  9. Simplify the fraction: Simplify the fraction 6784\frac{67}{84} to its simplest form.

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