Equations and inequalities: solving linear equations
The simplest equation to solve is a linear equation. A linear equation is an
equation where the power of the variable(letter, e.g.
$x$ ) is 1(one). The
following are examples of linear equations.
In this section, we will learn how to find the value of the variable that makes
both sides of the linear equation true. For example, what value of
$x$ makes
both sides of the very simple equation,
$x+1=1$ true.
Since the definition of a linear equation is that if the variable has a highest power of one (1), there is
at most
one solution or
root for the equation.
This section relies on all the methods we have already discussed: multiplying
out expressions, grouping terms and factorisation. Make sure that you arecomfortable with these methods, before trying out the work in the rest of this
chapter.
That is all that there is to solving linear equations.
Solving equations
When you have found the solution to an equation,
substitute the solution into the original equation, to check your answer.
Method: solving linear equations
The general steps to solve linear equations are:
Expand (Remove) all brackets that are in the equation.
"Move" all terms with the variable to the left hand side of the equation, and
all constant terms (the numbers) to the right hand side of the equals sign.Bearing in mind that the sign of the terms will change from (
$+$ ) to (
$-$ ) or vice
versa, as they "cross over" the equals sign.
Group all like terms together and simplify as much as possible.
If necessary factorise.
Find the solution and write down the answer(s).
Substitute solution into
original equation to check answer.
Solve for
$x$ :
$4-x=4$
We are given
$4-x=4$ and are required to solve for
$x$ .
Since there are no brackets, we can start with rearranging and then grouping like terms.
We are given
$\frac{2-x}{3x+1}=2$ and are required to solve for
$x$ .
Since there is a denominator of (
$3x+1$ ), we can start by multiplying both sides
of the equation by (
$3x+1$ ). But because division by 0 is not permissible, there
is a restriction on a value for x. (
$x\xe2\u2030\frac{-1}{3}$ )
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?