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Solve the equation (x)/(2) - (1)/(5) = (x)/(3) + (1)/(4) for x.

Mathematics

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Answer

2710\frac{27}{10}

Step-by-step solution

5 steps

To solve the equation x2−15=x3+14\frac{x}{2} - \frac{1}{5} = \frac{x}{3} + \frac{1}{4}, we need to find a common denominator for all fractions.

  1. Identify the denominators.

    The denominators are 2, 5, 3, and 4. The least common multiple (LCM) of 2, 5, 3, and 4 is 60.

  2. Multiply every term in the equation by the LCM (60) to eliminate the denominators.

    60(x2)−60(15)=60(x3)+60(14)60\left(\frac{x}{2}\right) - 60\left(\frac{1}{5}\right) = 60\left(\frac{x}{3}\right) + 60\left(\frac{1}{4}\right)

  3. Simplify each term.

    30x−12=20x+1530x - 12 = 20x + 15

  4. Move all terms containing xx to one side and all constant terms to the other side.

    Subtract 20x20x from both sides:

    30x−20x−12=1530x - 20x - 12 = 15 10x−12=1510x - 12 = 15

    Add 12 to both sides:

    10x=15+1210x = 15 + 12 10x=2710x = 27

  5. Solve for xx.

    Divide both sides by 10:

    x=2710x = \frac{27}{10}

    The final answer is 2710\frac{27}{10}.

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