Absolute Value of a number is its distance from zero on the number line. The absolute value of a number n is denoted by |n|.
Absolute value function is a piecewise function and is written as f (x) = |x|, where f(x) ≥ 0 for all values of x
This means that f (x) = - x for x < 0="" or="" f="" (x)="x" for="" x="" ≥="">
Absolute Value Inequalities: For all real numbers x and y, y > 0
1. if |x| < y,then="" -y="">< x=""><>
2. if |x| > y, then x > y or x <>
Absolute Value Equation: It is an equation of the form |ax + b| = c
Absolute Value: The absolute value of – 5 is 5, because – 5 is 5 units away from zero on the number line.
The absolute value of 6 is 6, because 6 is 6 units away from zero on the number line.
Absolute Value Function: y = |x| + 3
Absolute Value Inequalities: |m| > 5
Absolute Value Equation: |x - 3| = 6
Video Examples: Absolute Value 1
A. x < -="" 11="" or="" x=""> - 1
B. x > 11 or x <>
C. x < 11="" or="" x=""> 1
D. None of these
Correct Answer: B
Step 1: |6 - x| - 3 > 2 = |6 - x|> 5
Step 2: = - 5 > 6 - x > 5
Step 3: = - 5 - 6 > - x > 5 - 6
Step 4: = - 11 > - x > - 1
Step 5: = 11 < x=""><>
Step 6: = x > 11 or x <>
Q1: What is the value of |-9|?
Q2: Solve for x: |x| = 5
Q: What is the absolute value of -7?
A: The absolute value of -7 is 7, because -7 is 7 units away from zero.
Q: Can the absolute value of a number be negative?
A: No, the absolute value of a number is always non-negative.