In these properties on inequality, we have some properties. We can discuss the properties here.
In addition property, if x < y is there, we can add the same quantity on both side of the inequality.
i.e. x + z < y + z. for example 2 < 5 is there, we can add same number on both sides, i,e. 2 + 6 < 5 + 6.
In subtraction property, If x < y is there, we can subtract the same quantity on both sides of the inequality, that means, x – z < y – z. For example, 5 < 9 is there, we can subtract 3 on both sides of the inequality. 5 -3 < 9 – 3. In multiplication property, if x < y and z > 0 is there, then we can multiply by the same quantity z, that means x * z < y * z. In division property, If x < y and z > 0 is there, we can divide by the same quantity. That is, x/z < y/z. In transitive property, If x < y and y < z is there, then we can write the inequality as x < z. For example, 6 < 11 and 11< 19 then we can write it as 6 < 19. In comparison property, If x = y + z and z> 0 is there, then we can write it as x> y.
Examples:
1. Find, what property is demonstrated by the following statement?
4 < 7 and 7 < 10, thus 4 < 10.
2. Find, what property is demonstrated by the following statement?
10 = 7 + 3 then 10 > 4.