What is the solution set for the equation 8x + 15 = 7x + 12?

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Finding the Solution Set of the Equation

To solve the equation 8x + 15 = 7x + 12, we can follow these steps:

  1. Isolate the variable: Start by getting all terms containing x on one side and constant terms on the other.
  2. Subtract 7x from both sides:
    3. 8x + 15 - 7x = 7x + 12 - 7x

    This simplifies to:

    x + 15 = 12
  3. Subtract 15 from both sides:
    4. x + 15 - 15 = 12 - 15

    This further simplifies to:

    x = -3

The solution set for the equation 8x + 15 = 7x + 12 is:

  • {-3}

Thus, the only value that satisfies the equation is -3.

Conclusion

The solution set is concise; it consists of one element, which is -3. This means that when you substitute x = -3 back into the original equation, both sides will be equal, confirming that our solution is correct.

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