Solving Linear Equations Revision Notes for Leaving Cert Mathematics

Solving Linear Equations

Precedence of Operations

So far we have met the five basic operations of algebra - addition, subtraction, multiplication, division and exponentiation (or indices). Some operations come before others, we can refer to BIMDAS to see which ones to do first.

Example

infoNote

Solve for $x$ in $(x+1)^2+2(2(x-1)-4x)-x^2$

First we handle brackets - start with the most nested bracket

(x+1)^2+2(2\textcolor{red}{(x-1)}-4x)-x^2

Nothing to simplify, onto the other bracket :

(x+1)^2+2\textcolor{red}{(2(x-1)-4x)}-x^2

In here, we can simplify

(x+1)^2+2\textcolor{red}{(2x-2-4x)}-x^2

(x+1)^2+2\textcolor{red}{(-2x-2)}-x^2

There's nothing left to simplify in the brackets, we move onto indices :

(x+1)(x+1)+2{(-2x-2)}-x^2

Next is multiplication :

x^2+2x+1+2{(-2x-2)}-x^2

x^2+2x+1-4x-4-x^2

Addition and subtraction actually have the same precedence, clean up the expression from left to right :

-2x-3

Solving Linear Equations (Leaving Cert Mathematics): Revision Notes