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5x+72=3x2−145x + \frac{7}{2} = \frac{3x}{2} - 14 Find `x`

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Q. 5x+72=3x2−145x + \frac{7}{2} = \frac{3x}{2} - 14 Find `x`
  1. Get xx terms and constants: First, we want to get all the xx terms on one side and the constant terms on the other side. To do this, we can subtract 3x2\frac{3x}{2} from both sides of the equation.\newline5x+72−3x2=3x2−14−3x25x + \frac{7}{2} - \frac{3x}{2} = \frac{3x}{2} - 14 - \frac{3x}{2}\newlineThis simplifies to:\newline5x−3x2+72=−145x - \frac{3x}{2} + \frac{7}{2} = -14
  2. Combine like terms with common denominator: Now we need to combine like terms. To combine the xx terms, we need a common denominator. The common denominator for 5x5x and (3x/2)(3x/2) is 22, so we convert 5x5x to (10x/2)(10x/2).
    (10x/2)−(3x/2)+(7/2)=−14(10x/2) - (3x/2) + (7/2) = -14
    Now we can combine the xx terms:
    (10x/2)−(3x/2)=(7x/2)(10x/2) - (3x/2) = (7x/2)
    So the equation now is:
    (7x/2)+(7/2)=−14(7x/2) + (7/2) = -14
  3. Isolate x term by subtracting constants: Next, we want to isolate the xx term by subtracting 72\frac{7}{2} from both sides of the equation.\newline7x2+72−72=−14−72\frac{7x}{2} + \frac{7}{2} - \frac{7}{2} = -14 - \frac{7}{2}\newlineThis simplifies to:\newline7x2=−14−72\frac{7x}{2} = -14 - \frac{7}{2}
  4. Simplify right side of equation: Now we need to simplify the right side of the equation. To subtract (72)(\frac{7}{2}) from −14-14, we need to express −14-14 as a fraction with a denominator of 22. −14-14 is the same as (−282)(\frac{-28}{2}).
    (7x2)=(−282)−(72)(\frac{7x}{2}) = (\frac{-28}{2}) - (\frac{7}{2})
    Now we can subtract the fractions:
    (7x2)=(−282)−(72)=(−352)(\frac{7x}{2}) = (\frac{-28}{2}) - (\frac{7}{2}) = (\frac{-35}{2})
  5. Multiply by reciprocal to solve for xx: To solve for xx, we need to multiply both sides of the equation by the reciprocal of 72\frac{7}{2}, which is 27\frac{2}{7}.
    x=−352×27x = \frac{-35}{2} \times \frac{2}{7}
    Now we can multiply the numerators and denominators:
    x=−35×22×7x = \frac{-35 \times 2}{2 \times 7}
  6. Final division to find x: Simplify the multiplication:\newlinex=(−70)/14x = (-70) / 14\newlineNow we can divide −70-70 by 1414 to find xx:\newlinex=−5x = -5

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