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Solve the following equation for x. Express your answer in the simplest form. 4+3(-6x+6)=9+4(8x-6)

Solve the following equation for x x . Express your answer in the simplest form.\newline4+3(−6x+6)=9+4(8x−6) 4+3(-6 x+6)=9+4(8 x-6) \newline

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Full solution

Q. Solve the following equation for x x . Express your answer in the simplest form.\newline4+3(−6x+6)=9+4(8x−6) 4+3(-6 x+6)=9+4(8 x-6) \newline
  1. Expand left side: Expand the left side: 4+3(−6x+6)=4−18x+184 + 3(-6x + 6) = 4 - 18x + 18.
  2. Combine like terms left: Combine like terms on the left side: 4−18x+18=22−18x4 - 18x + 18 = 22 - 18x.
  3. Expand right side: Expand the right side: 9+4(8x−6)=9+32x−249 + 4(8x - 6) = 9 + 32x - 24.
  4. Combine like terms right: Combine like terms on the right side: 9+32x−24=32x−159 + 32x - 24 = 32x - 15.
  5. Set sides equal: Set the left side equal to the right side: 22−18x=32x−1522 - 18x = 32x - 15.
  6. Add xx terms: Add 18x18x to both sides to get the xx terms on one side: 22=50x−1522 = 50x - 15.
  7. Add to isolate x: Add 1515 to both sides to isolate the xx term: 37=50x37 = 50x.
  8. Divide to solve xx: Divide both sides by 5050 to solve for xx: x=3750x = \frac{37}{50}.

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