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x+7-(8x)/(3)=(17)/(6)-(5x)/(2)

x+7−8x3=176−5x2 x+7-\frac{8 x}{3}=\frac{17}{6}-\frac{5 x}{2}

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Full solution

Q. x+7−8x3=176−5x2 x+7-\frac{8 x}{3}=\frac{17}{6}-\frac{5 x}{2}
  1. Simplify terms: Simplify both sides of the equation by combining like terms.\newlineLeft side: x+7−(8x3)x + 7 - \left(\frac{8x}{3}\right)\newlineRight side: (176)−(5x2)\left(\frac{17}{6}\right) - \left(\frac{5x}{2}\right)
  2. Common denominator conversion: Convert all terms to have a common denominator to simplify the equation.\newlineLeft side: (3x3)+(213)−(8x3)=(−5x3)+(213)(\frac{3x}{3}) + (\frac{21}{3}) - (\frac{8x}{3}) = (\frac{-5x}{3}) + (\frac{21}{3})\newlineRight side: (176)−(15x6)=(176)−(15x6)(\frac{17}{6}) - (\frac{15x}{6}) = (\frac{17}{6}) - (\frac{15x}{6})
  3. Set expressions equal: Set the expressions equal to each other and solve for xx.−5x3+213=176−15x6\frac{-5x}{3} + \frac{21}{3} = \frac{17}{6} - \frac{15x}{6}Combine xx terms: −5x3+15x6=176−213\frac{-5x}{3} + \frac{15x}{6} = \frac{17}{6} - \frac{21}{3}
  4. Combine xx terms: Simplify further by finding a common denominator for xx terms and constants.\newline(−10x/6)+(15x/6)=(17/6)−(42/6)(-10x/6) + (15x/6) = (17/6) - (42/6)\newline(5x/6)=(−25/6)(5x/6) = (-25/6)\newlinex=(−25/6)/(5/6)x = (-25/6) / (5/6)\newlinex=−5x = -5

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