
Examples:
Example: Solve the double inequality 3 < 4(x + 2)  3 < 9 Solution: 3 < 4(x + 2)  3 < 9 Using distributive law 4(x + 2) can be written as 4x + 8 3 < 4x + 8  3 < 9 3 < 4x + 5 < 9 Subtracting 5 to all three terms and simplifying we get: 3  5 < 4x + 5  5 < 9  5 8 < 4x < 4 Dividing all three terms by 4 we get: 2 < x < 1 x >2 and x <1 implies that x ranges from 2 to 1. Directions: Solve for the variable in the inequalities given below. Write at least ten examples of your own and prove transitive property. 