Linear Equations that are fractions

Linear Equations that are Fractions

Introduction

  • Linear equations that are fractions involve an unknown variable such as x which is part of a fractional term.
  • These equations can either be a simple one-term fraction or a more complex multiple-term fraction. For instance, a simple fraction might look like this: x/4 = 2, while a more complex fraction could be 3x/2 -1 = 4.

Understanding Fractional Equations

  • As with any linear equation, the objective is to isolate x and solve for its value. In the case of fractional equations, the methods used often involve cross-multiplication or multiplication by the reciprocal.

Solving Linear Fractional Equations

  1. A common strategy in solving linear fractional equations is to multiply the entire equation by the denominator of the fraction where x resides. This can be used to neutralise the fraction, turning it into a standard linear equation.

  2. After turning it into a standard linear equation, you shall follow the normal steps to solve the linear equation such as addition, subtraction, multiplication or division, ensuring to apply the same function to both sides to maintain balance.

Examples

  • For the linear equation x/4 = 2, the first step would be to multiply both sides by 4 to cancel the fraction, resulting in x = 8. So, the solution is x = 8.
  • In another example, 3x/2 -1 = 4, first add 1 to both sides yielding 3x/2 = 5. Now multiply the entire equation by 2, you get 3x = 10. From here, divide everything by 3 to find the solution, leading to x = 10/3.

Conclusion

  • Solving linear fractional equations can seem daunting at first but becomes more manageable with repeated practice.
  • Consistent practice can help to solidify understanding and enhance problem-solving speed, which is an absolute necessity for complex algebraic problem-solving.
  • Just like solving linear equations, considering the rules of symmetry and maintaining balance in equations are crucial for correct problem-solving.
  • Mastering fractional equations often lays the groundwork for more advanced topics such as solving quadratic equations and rational equations.