- What are inequalities
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- Things which changes the direction of the inequality
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- Linear Inequation in One Variable
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- Linear Inequation in Two Variable
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- Quadratic Inequation
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- Steps to solve the inequalities in one variable
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- Steps to solve the inequality of the another form
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- Steps to solve Quadratic or polynomial inequalities
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- Absolute value equation
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- Absolute value inequation
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- Graphical Solution of Linear inequalities in Two Variable

Absolute value is denoted by |x|. And it is defined as

|x| = x if x $\geq$ 0

=-x if x < 0

So it is always positive.

**Examples**

|x-4|=2

or x-4=-2 or x-4=2

or x=2 or x =6

|x-2| > 4

|x| < 2

This is a form of Absolute value inequation

**Important Formula's**

for a and r being positive real number

|x| < a implies that -a< x< a

|x| > a implies that x< -a or x> a

|x| $\geq$ a implies that x $\geq$ a or x $\leq$ a

|x-a| < r implies that a-r < x < a+r

|x-a| > r implies that x < a-r or x > a+r

a< |x| < b implies that x lies in (-b,-a) or (a,b)

a< |x-c| < b implies that x lies in (-b+c,-a+c) or (a+c,b+c)

**Examples**

1) |x-2| > 4

**Solution**

we know from the Formula

|x-a| > r implies that x < a-r or x > a+r

So x < -2 or x > 6

2) |x| < 2

**Solution:**

We know that Formula

|x| < a implies that -a< x< a

So -2 < x < 2

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