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Use the transposition method to solve given linear equation in one variable:3(3x - 2)/3 + (2x + 3)/3 = x + 7/6

Question

Use the transposition method to solve given linear equation in one variable:

3(3x−2)3+(2x+3)3=x+76 \frac{3(3x - 2)}{3} + \frac{(2x + 3)}{3} = x + \frac{7}{6}

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Solution

Sure, let's solve the equation step by step.

  1. Simplify the equation:

    3(3x - 2)/3 + (2x + 3)/3 = x + 7/6

    This simplifies to:

    (3x - 2) + (2x + 3)/3 = x + 7/6

  2. Multiply through by 3 to get rid of the denominator:

    3x - 2 + 2x + 3 = 3x + 7/2

  3. Simplify the equation:

    5x + 1 = 3x + 7/2

  4. Subtract 3x from both sides:

    2x + 1 = 7/2

  5. Subtract 1 from both sides:

    2x = 7/2 - 2

  6. Simplify the right side:

    2x = 3/2

  7. Divide both sides by 2:

    x = 3/4

So, the solution to the equation is x = 3/4.

This problem has been solved

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