Solving Inequalities

Inequalities are the expressions that shows without using any equal sign means it will show as an expression that have signs of less than or greater than. Some times it is possible that these expression also have the equal sign but along with the less than or greater than sign that is also describe as a less than equal to or greater than equal to sign. Solving Inequalities having the same pattern like equations that is describe as an expression with the equal sign. One thing keep in the mind at the time of solving the inequality is that whenever change the side of the variable or values sign will change as > greater sign will change into the < and < less than sign will change into the > greater than sign.
There are some rules that does not effects the change of the sign as follows:
Whenever any number will be subtracted from any one of side then the same process is also done from other side.
When multiply both side of the inequality with positive number will also not effect the sign of inequality.
But there are also some ways that will change the sign as if multiply with the negative number or when we slide the number from one side to another side. we can simply define it by an example: 3 n < 7.
Now in the above inequality we have to put the values in place of n that satisfy inequality. there is no need to change in the sign.
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Solving Inequalities

If we have two values and both given values are not equal then we say that there is an inequality in both the values. Some of the conditions of an inequality are:

Suppose we have two variables ‘u’ and ‘v’. If u ≠ v; which represents u is not equal to v, and if u < v then we say that u is less than v, and if u > v then we say that u is greater then v. when u <= v, it means u is less than equal to v. When u >= v then u is greater than equal to v.

Now we will understand how to Solving Inequalities using multiplication and division? To find inequalities by multiplication and division we need to follow some steps which are shown below:

Step1: To solve inequality first of all we have to take an equation.

Step2: Remember that the inequality equation should only be defined in above symbols.

Step3: If equal sign is present in between the equation then the given equation never contain any inequality. Now we will understand it with the help of small example: (know more about Solving Inequalities, here)

Lets we have –a / 5 > 21; then solving inequalities by multiplication or division method. To solve inequality we need to follow all the above mention steps:

To find inequality first we have to take inequality, and if it has < or > signs then it is an inequality. So, the given equality can be written as:

= –a / 5 > 21,

To solve the inequality we have to multiply -5 on both sides of equation. On multiplying -5 we get:

= – a / 5 > 2,

= (-5) * -a / 5 > 21 * -5,

= 5a / 5 > -105, On further solving inequality we get:

If we divide 5 from 5 then we get 1. Now we have equation like this:

= a > -105, So it can be written as:

= a < -105. In this way we can solve inequality.

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Two Step Linear Inequality

Earlier we have discussed about verifying trigonometric identities and now we are going to start Two step Inequalities or two step equations which falls under gujarat secondary education board,They are the inequalities or equations which cannot be solved in single step operation. It involves the series of steps one after another to get the solution for the given variable in the equation. While we are solving inequality, we must remember that if any negative number is multiplied or the inequality is divided by any negative number, then the sign of inequality changes.
Now here are some equations and inequalities which can be solved by two steps:
2x + 4 = 10
In this equation, first we subtract 4 from both the sides,
We get the following form by solving equations :
   2x + 4 - 4 = 10 - 4
 or,  2x = 6
 This solution we get by the first step, but still the value of x is not obtained. So to obtain the value we proceed to second step of solution:

In second step we divide both sides of the equation by 2,
we get 2x / 2 = 6 /2
or x = 3 is the solution to the given equation.

Let us take another example:(Know more about Linear Inequality in broad manner here,)
35 = 5x - 10
Here in first step of solution, we add 10 to both sides of the given equation.
we get,
35 + 10 = 5x -10 + 10
or, 45 = 5x
Now in second step we divide both sides of the equation by 5
we get 45 / 5 = 5x/ 5
            9 = x is the solution of the given
Now let us take an example of Solving Two step Inequalities,
        3x -5 >= 16
For Solving Inequalities
   Add 5 to both sides we get
     3x - 5 + 5 > = 16 + 5
 or 3x  >= 21
Now we divide both sides of the inequality by 3,
we get
 3x /3 > = 21 / 3
 x > = 7 Ans.

This is all about two step equations and Inequalities. In the next article we are going to discuss about solving two step linear inequality and if anyone wants to know about Math Blog on Estimating Quotients then they can refer Internet.