Table of Contents
What does modulus mean in inequalities?
The modulus symbol is sometimes used in conjunction with inequalities. For example, |x| < 1. means all numbers whose actual size, irrespective of sign, is less than 1. This means any value. between −1 and 1.
How do you know if inequality is AND or OR?
If it is a conjunction that uses the word and, the solution must work in both inequalities and the solution is in the overlap region of the graph. If it is a disjunction that uses the word or, the solution must work in either one of the equations.
How do you know if an inequality is AND or OR?
What are some examples of solving inequalities with modulus?
Solving Inequalities with Modulus – Examples. Example 1 : Solve the absolute value inequality given below |x – 9| < 2. and express the solution in interval notation. Solution :-2 < x – 9 < 2. Add 9 throughout the equation-2 + 9 < x – 9 + 9 < 2 + 9. 7 < x < 11. Hence the solution set of the above absolute inequality is (7, 11). Example 2 :
How do you find the modulus of a given number?
Solution: Every modulus is a non-negative number and if two non-negative numbers add up to get zero then individual numbers itself equal to zero simultaneously. x 2 – 5x + 6 = 0 for x = 2 or 3 x 2 – 8x + 12 = 0 for x = 2 or 6
What are the properties of inequalities in math?
Two other useful properties concerning inequalities are: Example 2: If |x 2 – 5x + 6| + |x 2 – 8x + 12| = 0. Find x. Every modulus is a non-negative number and if two non-negative numbers add up to get zero then individual numbers itself equal to zero simultaneously.
What are the properties of modulus function?
Properties of Modulus Function. The modulus function has the following properties. 1. For any real number x, we have x 2 = ∣ x ∣ sqrt{x^2} = |x| x 2 = ∣ x ∣. 2. ∣ ∣ x ∣ ∣ = ∣ x ∣ ||x||=|x| ∣ ∣ x ∣ ∣ = ∣ x ∣. 3. If a and b are positive real numbers, then