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Solve the following equation for x. Express your answer in the simplest form. -5x-(8x-8)=3(4x-7)-2

Solve the following equation for x x . Express your answer in the simplest form.\newline−5x−(8x−8)=3(4x−7)−2 -5 x-(8 x-8)=3(4 x-7)-2 \newline

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Full solution

Q. Solve the following equation for x x . Express your answer in the simplest form.\newline−5x−(8x−8)=3(4x−7)−2 -5 x-(8 x-8)=3(4 x-7)-2 \newline
  1. Distribute 33 into expression: Now, distribute the 33 into (4x−7)(4x-7).\newline−5x−8x+8=12x−21−2-5x - 8x + 8 = 12x - 21 - 2
  2. Combine like terms: Combine like terms on both sides of the equation.\newline−13x+8=12x−23-13x + 8 = 12x - 23
  3. Add 13x13x to both sides: Add 13x13x to both sides to get all xx terms on one side.\newline−13x+13x+8=12x+13x−23-13x + 13x + 8 = 12x + 13x - 23
  4. Simplify the equation: Simplify the equation. 8=25x−238 = 25x - 23
  5. Add 2323 to isolate xx: Add 2323 to both sides to isolate the xx term.\newline8+23=25x−23+238 + 23 = 25x - 23 + 23
  6. Simplify the equation again: Simplify the equation again. 31=25x31 = 25x
  7. Divide by 2525 to solve: Divide both sides by 2525 to solve for xx.3125=25x25\frac{31}{25} = \frac{25x}{25}
  8. Divide by 2525 to solve: Divide both sides by 2525 to solve for xx.3125=25x25\frac{31}{25} = \frac{25x}{25}Simplify the division to find the value of xx.x=3125x = \frac{31}{25}

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