In the previous post we have discussed about Absolute Value Inequalities and In today's session we are going to discuss about How to solve linear inequalities. If graph of an equation is a straight line then equation is called as linear equation. For example: q = mp + c; here ‘m’ shows the slope of line and ‘c’ shows Y- intercept where line crosses q – axis (here ‘p’ is along to the horizontal axis and ‘q’ is along to vertical axis. If (<, >) these symbols are there in a linear expression then it comprise inequality in it. Now we will understand the concept of

Let’s understand the concept of solving systems of linear inequalities. Let's we have a linear inequality 4a + b < 15, then we can calculate this linear inequality as mention below:

In the above given linear inequality is there so after calculating, coordinates we found is under the line. Here set different values for one variable to get other coordinates. So it can be written as:

=> 4a + b < 15, to find coordinates of linear inequalities replace inequality symbol by equal sign.

=> b = 15 – 4a.

On putting value of a = 1 we get:

=> b = 15 – 4 (1),

=> b = 11.

On putting value of a = 3 we get:

=> b = 15 – 4 (3), on further solving we get:

=> b = 15 – 12,

=> b = 3.

In this way we can find different values. So here we get (1, 11), (3, 3). If we plot the graph we get inequalities below the line.

**linear inequalities**. It is fully depends on symbol that present in inequality. If less than sign present in linear expression then we found inequality under the line. If grater than sign is present in linear expression then we found inequalities top the line.Let’s understand the concept of solving systems of linear inequalities. Let's we have a linear inequality 4a + b < 15, then we can calculate this linear inequality as mention below:

In the above given linear inequality is there so after calculating, coordinates we found is under the line. Here set different values for one variable to get other coordinates. So it can be written as:

=> 4a + b < 15, to find coordinates of linear inequalities replace inequality symbol by equal sign.

=> b = 15 – 4a.

On putting value of a = 1 we get:

=> b = 15 – 4 (1),

=> b = 11.

On putting value of a = 3 we get:

=> b = 15 – 4 (3), on further solving we get:

=> b = 15 – 12,

=> b = 3.

In this way we can find different values. So here we get (1, 11), (3, 3). If we plot the graph we get inequalities below the line.

**Quantitative Analysis**can be defined as the determination of the absolute or relative value of one or several or all particular item present in a sample. icse syllabus 2013 is useful for icse students.
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