Solving Equations

posted on: 06 Mar, 2012 | updated on: 22 Sep, 2012

Solving Equations is the process of finding the values of the variables or unknown quantities that are satisfied by the condition defined in the equation. An equation is described as the Combination of the variables and the values, and these equations are solved by using three different ways: with the help of Algebra, by graphs, by using the concept of equivalence. There are several equations that define the different types of equations as:

a – 2 = 4 or

2 p – 4 = 16 or

3 s – 8 = 5 s – 6 or

3 / 4 a + 5 / 6 = 5 a - 125 / 3 or

2 (3 p – 7) + 4 (3 p + 2) = 6 (5 p + 9) + 3 or

6 a – 7/4 + 3 a – 5/7 = 5 a + 78/28 etc.

The above equations have variables like a, x, p or s. etc and the constant values that are joined with each other using some operations like addition / subtraction / multiplication / division. These types of equations are known as Linear Equations and we solve equations as follows:

If we take equations a + b = 2 a – 1 and a = b + 1 then the value of the variable a is calculated by putting the value b + 1 in place of a, so the equation is written as ( b + 1 ) + b = 2 ( b + 1 ) - 1.

Then in the equation only variable b is unknown and the value of b is equal to 0 thus we get the value of a that is equal to 1. So we can write it as (a, b) = (1, 0).

The process to solve equation that contains Radicals is shows below:

(a – 8) 1 / 2 = 3 is a radical equation and is solved by taking the Square of both sides of equality sign as ((a – 8) 1 / 2 ) 2 = ( 3 ) 2

a – 8 = 9

And a = 9 + 8

a = 17

(It should be remembered that we never take the square root of negative number).

We can take some examples of Solving Equations that have the absolute values:

| 2 a – 1 | = 5 is an equation of absolute value that can be solved in some steps.

Isolate the absolute value as: 2 a – 1 = 5 ------------- (1)

Or 2 a – 1 = - 5 ------------ (2)

Now solve equation (1): 2 a – 1 = 5

2 a= 6

a = 3

Solve equation (2): 2 a – 1 = - 5

2 a = - 4

a = -2

There are two solutions 3 and -2. Put them into the actual equation and find the answer as

| 2 a – 1 | = 5

| 2. 3 – 1 | = 5

| 6 – 1 | = 5

5 = 5 so the result is 5.

Topics Covered in Solving Equations

Equations With More Than One Variable

posted on: 16 Jul, 2012 | updated on: 17 Jul, 2012

When we write expressions of equations such that left side of expression is equal to right side of expression, then we call it equation. A linear equation is an equation which is written in form ax + b = 0 or ax + by = c
In order to solve Linear Equations with More Than One Variable, we say that values for variables of equation can be calculated by...Read More

Solutions and Solution Sets

posted on: 17 Jul, 2012 | updated on: 22 Sep, 2012

Solutions and solution Sets for any equation represented as Y = f (X) are pair of values of 'X' and corresponding values of 'Y'. These Sets are put in a parenthesis, separated by a comma as: (X, Y), with each and every Set satisfying the equation. For example, if you have an equation given as Y = 4X2, solution set can be given as: (1, 4) and (2, 16) because, ...Read More

Solving Equations by Multiplication

posted on: 21 Mar, 2012 | updated on: 30 Aug, 2012

If the equation consist of a single variable, then we find that the equation can be solved by shifting all the terms with variables on one side of the equation and the constant terms on the another side of the equation. Now we further check that if the variable has a constant value with it expressed in form of division, then we multiply both the sides...Read More

Solving Equations with Variables on Both Sides

posted on: 22 Mar, 2012 | updated on: 01 Sep, 2012

As we know solving the equations having variable on one side of the equation is quite easier. Now we will solve the equation with variable on the both side of the equation. This topic seems to be hard but if we know some basics it will become quite easier. For Solving Equations with variable on each side of the equation we use the basic add...Read More

Solving Multi-Step Equations

posted on: 23 Mar, 2012 | updated on: 11 Sep, 2012

An equation is the Combination of expression and the operators, which are equated on both sides of the equation. There are certain simple equations which are solved in single steps, but on other hand we come across certain equations, in which we get the value for the variables in multiple steps of procedures. The methods of solving such equations are called ...Read More

Solving Equation by Division

posted on: 23 Mar, 2012 | updated on: 11 May, 2012

When we say a word equation, it means some variables and constants equated with another value with ‘equal to’ sign. When we say that we are solving the equation, it means we need to separate all the constants on one side of the equation and the variables will come on another side of the equation.
Now a question arises that, what we Mean by finding the value...Read More

Solving Equation by Subtraction

posted on: 23 Mar, 2012 | updated on: 11 May, 2012

Linear equation is an equation with one variable and to solve the linear equation, we Mean to find the value of the variable which satisfies the given equation. There are different methods of solving the Linear Equations.
Any linear equation can be solved by either hit and trial method, in which we keep on putting different values of the variable in the...Read More

Direct and Indirect Variations

posted on: 24 Mar, 2012 | updated on: 01 May, 2012

If the cost of 5 pens is $ 50, then the cost of 7 pens is $ 70. Here we find that as the number of pens increases, the cost of the pens has also increased. In this situation we observe that as the value of the first variable is increased, the value of second variable also increases. Thus the situation is of direct variation. Similarly we look at another ex...Read More

Solving Literal Equations/Formulas

posted on: 26 Mar, 2012 | updated on: 31 Aug, 2012

To solve Literal equations we mainly use the same rules which we use in to solve a linear equation. Before solving literal equations, we should know the exact meaning of literal equation because literal equation is quite different from other equations. For solving literal equations the variables of the equations are rearranged for finding their values l...Read More

Solving Equations by Addition

posted on: 27 Mar, 2012 | updated on: 14 Jul, 2012

A linear equation consists of a variable and a constant value. In order to get the value for the variable, we need to solve the equation and get the value for the unknown variable. We come across the Linear Equations with one variable and sometimes we find the pair of equations with two variables whose value is to be calculated.
When we solve any equation...Read More