Graphing Absolute Value Inequalities

Introduction to graphing absolute value inequalities:

Graphing absolute value inequalities is nothing but we are going to graph the solutions of the absolute value inequalities. To graph the absolute value inequalities first we have to find the solutions and using that we have to graph. Here we are going to learn about the graphing of absolute value inequalities. We will see some example problems for graphing the absolute value inequalities.

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Example Problems for Graphing Absolute Value Inequalities:

The main difference between the inequalities and equalities is we can say the range of the solutions in the inequalities. But in equalities we can determine the exact solution.

Example 1 for graphing absolute value inequalities:

Graph the absolute values of the inequalities. |x +2| `lt=` 8

Solution:

Given inequality is |x + 2| `lt=` 8

To find the absolute value for the given inequality

(x + 2) `lt=` 8 ………… (1) And –(x + 2) `lt=` 8 …………………. (2)

Equation 1:

(x + 2) `lt=` 8 ………… (1)

Add - 2 on both sides

x + 2 - 2 `lt=` 8 - 2

x `lt=` 6

Equation 2:

-(x + 2) `lt=` 8

-x - 2 `lt=` 8

Add +2 on both sides.

-x - 2 + 2 `lt=` 8 + 2

-x `lt=` 10

Divide by -1.

x `gt=` -10

So x lies between -10 `lt=` x `lt=` 6

We will see some more example problems bfor graphing the absolute value inequalities.

Example 2 for Absolute Value Inequalities:

Find the absolute values of the inequalities. |x - 6| `gt=` 5

Solution:

Given inequality is |x - 6| `gt=` 5

To find the absolute value for the given inequality

(x – 6) `gt= ` 5 ………… (1) And –(x – 6) `gt=` 5 …………………. (2)

Equation 1:

(x – 6) `gt=` 5 ………… (1)

Add +6 on both sides

x - 6 + 6 `gt=` 5 + 6

x `gt=` 11

Equation 2:

-(x – 6) `gt=` 5

-x + 6 `gt=` 5

Add -6 on both sides.

-x + 6 - 6 `gt=` 5 - 6

-x `gt=` -1

Divide by -1.

x `lt=` 1

So x lies between 1 `gt=` x `gt=` 11