Solving Absolute Value Inequalities

Introduction to solving absolute value inequalities:

Solving absolute value inequalities is nothing but the value without considering its sign. Here we are going to learn how we are solving absolute value inequalities. The main difference between the equalities and inequalities is less than and greater than symbol. We will see some example problem for solving absolute value inequalities. For graphing the absolute value inequalities we will use the number lines.

Example Problems for Solving Absolute Value Inequalities:

Solving absolute value inequalities example 1:

Solve the following |x + 5| `gt=` 5

Solution:

Here we are having the inequality |x + 5| `gt= ` 5

If we write these inequalities in absolute value form we will get

x + 5 `gt=` 5 ………… (1) And - (x + 5) `gt=` 5 ………….. (2)

Equation 1:

x + 5 `gt=` 5

Add -5 on both sides we will get

x + 5 – 5 `gt=` 5 – 5

x `gt=` 0

Equation 2:

-(X + 5) `gt=` 5

Add+5 on both sides we will get

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

-x > = 10

Divide by -1 so

x `lt= ` -10

So the x lies between 0 and -10

-10 `gt=` x `gt=` 0

We can mark these inequalities using the number line.

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Solving Absolute Value Inequalities Example 2:

Solve the following |x + 3| `gt=` 9

Solution:

Here we are having the inequality |x + 3|` gt= ` 9

If we write these inequalities in absolute value form we will get

x + 3 `gt=` 9 ………… (1) And -(x + 3)` gt= ` 9 ………….. (2)

Equation 1:

x + 3 `gt= ` 9

Add -3 on both sides we will get

x + 3 – 3` gt=` 9 – 3

x` gt=` 6

Equation 2:

- (X + 3) `gt=` 9

Add +3 on both sides we will get

-x - 3 + 3 `gt=` 9 + 3

-x `gt= ` 12

Divide by -1 so

x `lt=` -12

So the x lies between 0 and -12

-12 `gt=` x` gt=` 0

These are the some examples for solving absolute value inequalities. We can mark these absolute value inequalities in number line.