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When we represent an absolute value in the form of equation and inequalities then it is known as

value equation and inequalities

If x and y are two real numbers then

i) | x + y | ≤ | x | + | y |

ii) | x – y | ≤ | x | + | y |

iii) | x y | = | x | | y |

iv) If x = y then | x – y | = 0 and conversely, | x – y | = 0

v) If | x | ≤ y then – y ≤ x ≤ y

vi If | x | ≥ y then either x ≥ y or, x ≤ - y.

vii) | x – a | = b implies that either x = a + b or, x = a – b

Case 1: - + x < 1 So x < 1 … (1)

Case 2: - - x < 1 so x > -1 … (2)

From (1) and (2), we can write

-1 < x < 1