Linear Equations with brackets

Linear Equations with Brackets

Understanding the Concept

  • A Linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable.

  • Linear equations can often contain variables inside brackets. Solving these requires a combination of the techniques of expanding brackets and solving linear equations.

Formation of Linear Equations with Brackets

  • Linear equations with brackets often appear in the form of a(bx + c) = d, where ‘a’, ‘b’, ‘c’ and ‘d’ are constants and ‘x’ is the variable you need to solve for.

  • The real task is to isolate ‘x’ by following a systematic process of expanding the equation and simplifying it.

Solving Linear Equations with Brackets - Step by Step Guide

  1. Begin by expanding the brackets. This is achieved by multiplying the term outside the brackets with each term inside the brackets.

  2. The next step involves simplifying the equation by gathering all x terms on one side and constants on the other side of the equation.

  3. To find the value of ‘x’, divide both sides of the equation by the coefficient of ‘x’.

Examples

  • In the equation 3(2x + 4) = 18, the first step is to expand the brackets leading to 6x + 12 = 18. The next step involves simplifying to 6x = 18 - 12, ending with 6x = 6. Finally, divide both sides by 6, getting x = 1, which is the solution.

Remember

  • Always follow the rule of BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) while simplifying any algebraic equation.

  • Regular practice can be key to mastering algebraic equations including those with brackets and linear variables. Always take time to verify your answers.

Conclusion

  • Understanding and solving linear equations with brackets is an essential algebraic skill, which is used extensively in higher level mathematics.

  • It’s always useful to check your solution by substituting the value of ‘x’ back into the original equation to see if the sides balance. This ensures that you have correctly solved the equation.