1) Variables Intro
2) Dependent/Independent Variable
3) Manipulating Expressions/Equations
In Algebra and in Math, variables can appear in a range of formulas and expressions.
They are often written as letters of the alphabet, for example a , b , x , y.
As the name variable implies, the value of these letters can vary.
Variables in Algebra can be assigned any value or set of values, the value or values aren’t known initially.
In the expression x + 3 = 5, the variable present is x.
Even though for in equation such as this, the value of x can be seen to be only 2.
It is still referred to as a variable.
What are Variables in Algebra
Dependent, Independent
A variable can be classed as dependent or independent.
With y = 2x + 6,x is an independent variable, as such it could be assigned a range of possible values.
However, y is a dependent variable.
As the value of y depends on what value is given to x.
The value of y is dependent on the value of x.
Manipulating Expressions and Equations
with Variables
Other sections and pages on the site do go into a bit more detail about manipulating expressions and equations in order to solve for certain variables.
But this page will give a basic run through and introduction to some examples of how to approach finding the value of variables in Algebra.
Using some of the properties of equality.
Say you have a variable in a basic equation labelled x,
to solve for this x.
We would want try and structure the equation into the form x =”.
Examples of such situations using some of the properties of equality are shown below.
Examples
1.1
If a = b then a + c = b + c .
1) x + 2 = 7 , can subtract 2 from both sides to have the form “x =”.
x + 2 − 2 = 7 − 2 => x = 5
2) x − 1 = 8 , can add 1 to both sides.
x − 1 + 1 = 8 + 1 => x = 9
1.2
If a = b then a × c = b × c .
\boldsymbol{\frac{x}{2}} = 6 , can multiply both sides by 2.
\boldsymbol{\frac{x}{2}} × 2 = 6 × 2 => x = 12
1.3
If a = b then \bf{\frac{a}{c}} = \bf{\frac{b}{c}}.
1) 4x = 12 , can divide both sides by 4.
\boldsymbol{\frac{4x}{4}} = \bf{\frac{12}{4}} => x = 3
2) –2x = 4 , can divide both sides by -2.
\boldsymbol{\frac{{\text{-}}2x}{{\text{-}}2}} = \bf{\frac{4}{{\text{-}}2}} => x = –2
1.4
If a = b then a − b = 0.
4x − 8 = 0 , can move 8 across, then divide.
4x = 8 => \boldsymbol{\frac{4x}{4}} = \bf{\frac{8}{4}} => x = 2
1.5
2x = 3 + x , can move x across, to have the like terms on the same side.
2x − x = 3 => x = 3