Algebra Absolute Value Inequalities

Algebra absolute value inequalities are nothing but the absolute value inequalities using the algebraic expression. Here we are going to see how to solve absolute value inequalities in algebra. We will see some example problems foe algebra absolute value inequalities. It is better to understand the inequalities. Normally absolute value mean without considering the sign of the value. For example |x| = `+-x`

Example problems for algebra absolute value inequalities:

Example 1 for algebra absolute value inequalities:

Solve the following |x + 3| `gt=` 5

Solution:

Given equation is |x + 3| `gt=` 5

We can divide these into two parts.

(x + 3) `gt=` 5 and - (x +3) `gt=` 5

First part:

If we take the first part (x + 3) `gt=` 5

Add -3 on both sides

We get x + 3 – 3 `gt=` 5 – 3

x `gt=` 2

Second part:

- (x +3) `gt=` 5

-x – 3 `gt=` 5

Add +3 on both sides

-x – 3 + 3 `gt=` 5 + 3

-x `gt=` 8

So x `lt=` -8

So the solution is -8 `gt=` x `gt=` 2

We will see some more examples for Solving Absolute Value Inequalities. It is better to understand the concept.

Example 2 for algebra absolute value inequalities:

Solve the following |x - 9| `lt= ` 2

Solution:

Given equation is |x - 9| <= 2

We can divide these into two parts.

(x - 9) `lt=` 2 and - (x - 9) `lt= ` 2

First part:

If we take the first part (x - 9) `lt=` 2

Add + 9 on both sides

We get (x – 9 + 9) `lt=` 2 + 9

x `lt= ` 11

Second part:

- (x - 9) `lt=` 2

-x + 9 `lt=` 2

Add -9 on both sides

-x + 9 – 9 `lt=` 2 - 9

-x`lt=` -7

So x `gt=` 7

So the solution is 7`lt=` x `lt=` 11

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These are some of the example for algebra absolute value inequalities. From this we can understand how to solve the algebra absolute value inequalities.