SOLUTION: Solve the following compound inequality and show the solution on a number line and in interval notation. 2x+5>=7 and 3x<=9

To solve the compound inequality, you need to solve EACH inequality SEPARATELY and then TO TAKE THE INTERSECTION of their solution domains 

as the final solution to the compound inequality.


1)  2x + 5 > 7.    Subtract 5 from both sides. You will get an equivalent inequality

    2x < 7 - 5,
 
    2x < 2.        Now divide both sides by 2.  You will get an equivalent inequality

    x < 1.


    It is the solution of the first part of your compound inequality.


2)  3x < 9.        Divide both sides by 3.  You will get an equivalent inequality

     x < 3.


3)  Now you have two solution domains for separate inequalities:

      - the solution domain for the first inequality  x < 1,     and

      - the solution domain for the second inequality  x < 3.


    Their intersection is the domain  x < 1.

    It is the final solution to your original compound inequality.

    In the interval form it is (,).