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. (
$x\xe2\u2030\frac{-1}{3}$ )
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the
fraction, the value of the fraction becomes 2/3. Find the original fraction.
2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point For:
(6111,4111,−411)(6111,4111,-411)
Equation Form:
x=6111,y=4111,z=−411x=6111,y=4111,z=-411
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=