6.1  Solving Inequalities in One Variable

Mrs. Agriesti's Algebra

Goal: To learn to solve and graph inequalities in one variable.

An Inequality is similar to an equation but instead of "=" an inequality has "<, >, <, or >."

Examples:  Solve and graph each inequality. 

Ex 1:   x + 8 < 15
           x + 8 < 15
               - 8    - 8
                 x <  7

Your goal is to get the x by itself.
Use the same steps you would use for an equation.

There is no equal so use an open circle when graphing.

Ex 2:   5x + 3 > 7
            5x - 3 > 7
                + 3  +3
                 5x > 10
                 5x > 10         
                 5       5
                   x > 2

Your goal is to get the x by itself.
Use the same steps you would use for an equation.

There is no equal so use an open circle when graphing.

Ex 3:   13 - 7x < - 8
            13 - 7x <  - 8
           -13            -13
                - 7x  <  -21
                 -7x  <  -21         
                 -7        -7
                      x > 3

Your goal is to get the x by itself.
Use the same steps you would use for an equation.

Don't forget to switch the inequality after dividing by a negative number.

There is an equal so use a closed circle when graphing.

Ex 4:   3x > 11x + 4
            3x > 11x + 4
         -11x   -11x           
         - 8x  >  4
          -8x  >  4         
          -8       -8
              x < -1/2

Your goal is to get the x by itself.
Use the same steps you would use for an equation.

Don't forget to switch the inequality after dividing by a negative number.

There is an equal so use a closed circle when graphing.