Solving and Gaphing Compound Inequalities

The compound inequality is two or more inequalities joined together by conjunction or disjunction. Conjunction means “And” which shows that both statements of the compound sentence are true at the same time. It is the intersection of the result sets for the individual statement.  “Or” denotes the disjunction which means that, as long as either statement is true, the entire compound sentence is true. It is the combination or union of the answer sets for the individual statements. We will see about solving and graphing compound inequalities with few examples.

Solving and graphing compound inequalities Example problems:

Example 1 :
    Solve the compound inequality: 5x-6<9 and="" x="">23
Solution:
Step 1: Solve the first inequality
              5x-6<9 6="" both="" dd="" on="" p="" sides="">              5x-6+6<9 p="">                5x<15 p="">             Divide by 5 on both sides,
               `(5x)/5` <`15/5`
              x<3 p=""> Step 2: solve the second inequality
                 x+15>23 (Subtract 15 from both sides)
              x+15-15>23-15
                   x>8
The final solution is:
            3>x>8
This means that all numbers between 3 and 8 are solutions
                     Solving and graphing compound inequalities 5x-6<9 and="" x="">23,

                                       
Example 2:
      Solve the compound inequality 2x - 3 < 11   or 5x > 25
Solution:
Step 1: Solve the first inequality
               2x - 3 < 11
Add 3 on both sides
             2x - 3 +3< 11   +3
             2x<14 p=""> Divide by 2 on both sides,
            ` (2x)/2` <`14/2`
               x<7 p=""> Step 2: Solve the second inequality
            5x > 25
Divide by 5 on both sides
            `(5x)/5` > `25/5`
               y>5
The final solution is 7>x>5 which means that all number not between 5 and 7 are solutions.
                     Solving and graphing compound inequalities 2x - 3 < 11   or 5x > 25,
              

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Solving and graphing compound inequalities Continued:

Example 3:
      Solve the compound inequality  -13 < 4x+5 and x + 15 <23 p=""> Solution:
Step 1: Solve the first inequality
               -13 < 4x+5
 Subtract 5 from both sides
             -13 -5< 4x+5-5
                -18<4x nbsp="" p=""> Divide by 4 on both sides,
             -`18/4` < `(4x)/4`              
           -`9/2` Step 2: Solve the second inequality
            x + 15 < 23
   Subtract 15 on both sides,
    x + 15 - 15 < 23 -15
            x<8 p="">            Solving and graphing compound inequalities -13 < 4x+5 and x + 15 <23 strong="">,

                    
The final solution is 8>x>-`9/2` which means that all number t between -9/2 and 8 are solutions