How do you solve the equation 2/5 + (3x)/5 = (x + 5)/10 for x?

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To solve the equation 2/5 + 3x/5 = (x + 5)/10, we can follow these steps:

  1. Eliminate the fractions: To make the equation easier to work with, we can eliminate the fractions by multiplying every term by 10, which is the least common multiple of the denominators (5 and 10).
  2. This gives us:
    • 10 * (2/5) + 10 * (3x/5) = 10 * ((x + 5)/10)
  3. Simplifying the equation:
    • 10 * (2/5) = 4
    • 10 * (3x/5) = 6x
    • 10 * ((x + 5)/10) = x + 5
  4. So now the equation becomes:
    • 4 + 6x = x + 5
  5. Rearranging the equation: To isolate x, we can move the ‘x’ term to one side and the constant to the other:
    • 6x – x = 5 – 4
  6. This simplifies to:
    • 5x = 1
  7. Solving for x: Finally, divide both sides by 5:
    • x = 1/5

Therefore, the solution to the equation 2/5 + 3x/5 = (x + 5)/10 is x = 1/5.

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