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Solve the following equation for x. Express your answer in the simplest form. -5x-(1)/(2)(6x+8)=-7x+8(5x-5)

Solve the following equation for x x . Express your answer in the simplest form.\newline−5x−12(6x+8)=−7x+8(5x−5) -5 x-\frac{1}{2}(6 x+8)=-7 x+8(5 x-5) \newline

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Q. Solve the following equation for x x . Express your answer in the simplest form.\newline−5x−12(6x+8)=−7x+8(5x−5) -5 x-\frac{1}{2}(6 x+8)=-7 x+8(5 x-5) \newline
  1. Distribute and Simplify: First, distribute the −12-\frac{1}{2} across the (6x+8)(6x + 8). \newline−5x−(12)6x−(12)8=−7x+8⋅5x−8⋅5-5x - \left(\frac{1}{2}\right)6x - \left(\frac{1}{2}\right)8 = -7x + 8\cdot5x - 8\cdot5
  2. Combine Like Terms: Simplify the distributed terms.\newline−5x−3x−4=−7x+40x−40-5x - 3x - 4 = -7x + 40x - 40
  3. Add/Subtract Terms: Combine like terms on both sides.\newline−8x−4=33x−40-8x - 4 = 33x - 40
  4. Isolate x Term: Add 8x8x to both sides to get the x terms on one side.\newline−8x+8x−4=33x+8x−40-8x + 8x - 4 = 33x + 8x - 40
  5. Add/Subtract to Isolate xx: Simplify the equation after adding 8x8x to both sides.\newline−4=41x−40-4 = 41x - 40
  6. Simplify Equation: Add 4040 to both sides to isolate the xx term.\newline−4+40=41x−40+40-4 + 40 = 41x - 40 + 40
  7. Add/Subtract to Isolate xx: Simplify the equation after adding 4040 to both sides.\newline36=41x36 = 41x
  8. Simplify Equation: Divide both sides by 4141 to solve for xx. \newline3641=41x41\frac{36}{41} = \frac{41x}{41}
  9. Divide to Solve for x: Simplify the equation after dividing by 4141.x=3641x = \frac{36}{41}

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