Equation is a combination of one or more terms separated with equal"=" symbol. Terms can be numerical, alphanumerical, expression etc.
For Example :
4 + 8 = 3 * 4
or
ax/1 = 0 + ax (values on bothe the sides remains the same)
Problems involving equations are needed across grades and levels. Quadratic, Linear, Polynomial and Differential equations need a through understanding of basic and advanced Math concepts by students.
And (algebraic) equation is a statement that two expressions are equal.
It may involve one or more than one variables (literal number)
Thus 2x – 3 = 1 + x, p2 + p + 1 = 3 are equations in one variable,
2x + 3y = 13, x2 + y2 + 2xy = 4 are equations in two variables,
while stu = 20 is an equation in three variables
An equation containing only one variable (literal) with highest power 1 is called a linear equation in that variable
One more example:- 3x + 5 = 8, 3 – 2x = 5x + 1and 4n = 2/3n – 1 are all linear equations in one variable.
In this chapter, we shall take up simple equations in one variable only.
Solving An Equation
A number which satisfies the given equation is called a solution or root of the equation.
‘Satisfying the equation’ means that if the variable (literal) involved in the equation is replaced by the number, then both sides of the equation become equal.
The process of finding the particular value of the variable (literal) which makes both sides of the equation equal is called solving the equation.
Consider the equation x + 3 = 5
What particular value of x would make this equation true?
We can try to solve it by trial and error method
Let us try x = 0. Then left hand side (L.H.S.) = 0 + 3 = 3, while right hand side (R.H.S.) = 5. So x = 0 is not a solution
Now let us try x = 1. Then L.H.S. = 1 + 3 = 4 while R.H.S. = 5
Now let us try x = 2. Then L.H.S. = 2 + 3 = 5 and R.H.S. = 5
So x = 2 is a solution of the equation x + 3 = 5
You can immediately see that this method of trial and error can be time consuming. Let us find a much better method.
You must be familiar with how a weighing balance works. When the weights in two sides are equal, the balance is balanced (what else?). Then you can add equal weights to both sides and still the two sides will hang in balance. You can remove equal weights from both sides, and still the two sides will hang in balance. We can apply these ideas to algebraic equations.
Rule 1:- If equals are added to equals, the sums are equals. In other words, you can add the same number to both sides of an equation.
Rule 2:- If equals are subtracted from equals, the remainders are equal. In other words, you can subtract the same number from both sides of and equation.
Rule 3:- The two sides of an equation may be multiplied by same non-zero number For example, if x/5 = 7, then x/5 × 5 = 7 × 5.
Rule 4:- The two sides of an equation may be divided by same non-zero number
For example, if 3x = 12, then 3x/3 = 12/3
Now let us solve a number of equations using these rules.
Learn how to solve equation
There are various methods of solving an equation. These include the Trail and Error Method, The Taylor method, Numerical Method, Solving Equations using Inverse Functions or principals of Elementary Algebra.
TutorVista's tutors will share all the tips and techniques to make solving an equation easy and simple. Our tutors are subject experts and have many years of experience in tutoring students across grades and levels. Our Math tutors will only explain basic and advanced Math concepts but will also be available for everyday homework and assignment help or last minute assistance before important tests or assignments.
So however complicated the equation you need help with is our tutors can help!
Example 1: Solve
2(x + 3) = 12
2x + 6 = 12
2x = 12 - 6
2x = 6
x = 6/2
x = 3
Solving Equation
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Example 2: Solve
x2 + 5x + 6 = 0
x2 + 2x + 3x + 6 = 0
x(x + 2) + 3(x + 3) = 0
(x + 2) (x + 3) = 0
x + 2 = 0 or x + 3 = 0
x = 0 - 2 or x = 0 - 3
x = 2 or x = - 3
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