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Solve for x and write your answer in simplest form. -(3)/(2)-(-(1)/(2)x+10)+x=9x Answer: x=

Solve for x x and write your answer in simplest form.\newline−32−(−12x+10)+x=9x -\frac{3}{2}-\left(-\frac{1}{2} x+10\right)+x=9 x \newlineAnswer: x= x=

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Q. Solve for x x and write your answer in simplest form.\newline−32−(−12x+10)+x=9x -\frac{3}{2}-\left(-\frac{1}{2} x+10\right)+x=9 x \newlineAnswer: x= x=
  1. Distribute and Combine Like Terms: Simplify the left side of the equation by distributing the negative sign and combining like terms.\newlineWe have the equation: −(32)−(−(12)x+10)+x=9x-(\frac{3}{2})-(-(\frac{1}{2})x+10)+x=9x\newlineDistribute the negative sign through the parentheses: −(32)+(12)x−10+x=9x-(\frac{3}{2}) + (\frac{1}{2})x - 10 + x = 9x\newlineCombine like terms: (12)x+x=(32)x(\frac{1}{2})x + x = (\frac{3}{2})x\newlineNow the equation is: −(32)+(32)x−10=9x-(\frac{3}{2}) + (\frac{3}{2})x - 10 = 9x
  2. Add to Isolate x Terms: Add (32)(\frac{3}{2}) to both sides to isolate the x terms on one side.\newline−32+32x−10+32=9x+32-\frac{3}{2} + \frac{3}{2}x - 10 + \frac{3}{2} = 9x + \frac{3}{2}\newlineThis simplifies to: 32x−10=9x+32\frac{3}{2}x - 10 = 9x + \frac{3}{2}
  3. Add 1010 to Isolate x Terms: Add 1010 to both sides to further isolate the xx terms.\newline32x−10+10=9x+32+10 \frac{3}{2}x - 10 + 10 = 9x + \frac{3}{2} + 10 \newlineThis simplifies to: 32x=9x+32+10 \frac{3}{2}x = 9x + \frac{3}{2} + 10
  4. Subtract to Combine xx Terms: Subtract 32x\frac{3}{2}x from both sides to get all xx terms on one side.\newline32x−32x=9x+32+10−32x\frac{3}{2}x - \frac{3}{2}x = 9x + \frac{3}{2} + 10 - \frac{3}{2}x\newlineThis simplifies to: 0=9x−32x+32+100 = 9x - \frac{3}{2}x + \frac{3}{2} + 10
  5. Combine Like Terms: Combine like terms on the right side.\newline0=9x−32x+32+100 = 9x - \frac{3}{2}x + \frac{3}{2} + 10\newlineTo combine the x terms, convert 9x9x to 182x\frac{18}{2}x so that we have a common denominator:\newline0=182x−32x+32+100 = \frac{18}{2}x - \frac{3}{2}x + \frac{3}{2} + 10\newlineNow combine the x terms: 182x−32x=152x\frac{18}{2}x - \frac{3}{2}x = \frac{15}{2}x\newlineSo the equation is now: 0=152x+32+100 = \frac{15}{2}x + \frac{3}{2} + 10
  6. Subtract to Isolate x Term: Subtract (32)(\frac{3}{2}) from both sides to isolate the x term.\newline0−32=152x+32+10−320 - \frac{3}{2} = \frac{15}{2}x + \frac{3}{2} + 10 - \frac{3}{2}\newlineThis simplifies to: −32=152x+10-\frac{3}{2} = \frac{15}{2}x + 10
  7. Subtract to Isolate x Term: Subtract 1010 from both sides to completely isolate the xx term.\newline−32−10=152x+10−10-\frac{3}{2} - 10 = \frac{15}{2}x + 10 - 10\newlineThis simplifies to: −32−10=152x-\frac{3}{2} - 10 = \frac{15}{2}x
  8. Combine Numbers on Left: Convert −10-10 to a fraction with a denominator of 22 to combine with −(3)/(2)-(3)/(2). \newline−10=−(20)/(2)-10 = -(20)/(2)\newlineNow the equation is: −(3)/(2)−(20)/(2)=(15)/(2)x-(3)/(2) - (20)/(2) = (15)/(2)x\newlineCombine the numbers on the left side: −(23)/(2)=(15)/(2)x-(23)/(2) = (15)/(2)x
  9. Divide to Solve for x: Divide both sides by (152)(\frac{15}{2}) to solve for x.\newlinex=−(232)(152)x = \frac{-\left(\frac{23}{2}\right)}{\left(\frac{15}{2}\right)}\newlineTo divide by a fraction, multiply by its reciprocal: x=−(232)×(215)x = -\left(\frac{23}{2}\right) \times \left(\frac{2}{15}\right)
  10. Simplify the Fraction: Multiply the numerators and denominators. \newlinex=−(23)×22×15x = \frac{{-(23) \times 2}}{{2 \times 15}}\newlineThis simplifies to: x=−4630x = \frac{{-46}}{{30}}
  11. Simplify the Fraction: Multiply the numerators and denominators.\newlinex=−(23)×22×15x = \frac{-(23) \times 2}{2 \times 15}\newlineThis simplifies to: x=−4630x = \frac{-46}{30} Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 22.\newlinex=(−46/2)(30/2)x = \frac{(-46 / 2)}{(30 / 2)}\newlineThis simplifies to: x=−2315x = \frac{-23}{15}

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