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. (
$x\xe2\u2030\frac{-1}{3}$ )
not much
For functions, there are two conditions for a function to be the inverse function:
1--- g(f(x)) = x for all x in the domain of f
2---f(g(x)) = x for all x in the domain of g Notice in both cases you will get back to the element that you started with, namely, x.
Grace
sin theta=3/4.prove that sec square theta barabar 1 + tan square theta by cosec square theta minus cos square theta
@dashawn ... in simple terms, a derivative is the tangent line of the function. which gives the rate of change at that instant. to calculate. given f(x)==ax^n. then f'(x)=n*ax^n-1 . hope that help.
Christopher
thanks bro
Dashawn
maybe when i start calculus in a few months i won't be that lost 😎
In this morden time nanotechnology used in many field .
1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc
2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc
3- Atomobile -MEMS, Coating on car etc.
and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.