(7/2x-2)-(3/2x-1)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (7/2x - 2) - (3/2x - 1)

This article will guide you through the process of simplifying the algebraic expression: (7/2x - 2) - (3/2x - 1).

Understanding the Expression

The expression involves fractions with variables in the denominator. We need to simplify it by combining like terms and performing the necessary operations.

Steps to Simplify

1. Distribute the negative sign:

   • The negative sign in front of the second parenthesis means we multiply each term inside by -1.
   • This gives us: (7/2x - 2) + (-3/2x + 1)

2. Combine like terms:

   • Group the terms with 'x' together and the constant terms together.
   • This leads to: (7/2x - 3/2x) + (-2 + 1)

3. Simplify:

   • Combine the coefficients of 'x': (7/2 - 3/2)x = 2x
   • Combine the constant terms: -2 + 1 = -1

4. Final Result:

   • The simplified expression is: 2x - 1

Conclusion

By following the steps above, we have successfully simplified the expression (7/2x - 2) - (3/2x - 1) to 2x - 1. Remember to always distribute the negative sign and combine like terms to achieve a simplified form.